Labour/Labor Variances - Formulae Review - Illustration
Approach
Factually, our problem solving capability is limited by our ability to interpret the problem. Whatever may be the way the problem is presented (what we call problem models), if we can arrange the information into the working table, the rest of the task becomes easy.
Understanding the meaning of the variance helps derive the formula for calculating the variance even if we fail recollecting.
Recalculating Standards
Building the following working table amounts to recalculating standards for both actual inputs and actual outputs. It enables us to use the simplest formulae involving costs for deriving the variances. It helps us solve almost all problems in a similar manner.Standard | Actual | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
for SO | for AO | for AI | Total | Idle (Abnormal) | Productive | |||||||||
ST | SR | ST(AO) | SC(AO) | ST(AI) | SC(AI) | AT | AR | AC | SC(AT) | IT | SC(IT) | PT | SC(PT) | |
Factor | (AO) | (AI) | ||||||||||||
Skilled Semi-Skilled Unskilled | STsk STss STus | SRsk SRss SRus | ST(AO)sk ST(AO)ss ST(AO)us | SC(AO)sk SC(AO)ss SC(AO)us | ST(AI)sk ST(AI)ss ST(AI)us | SC(AI)sk SC(AI)ss SC(AI)us | ATsk ATss ATus | ARsk ARss ARus | ACsk ACss ACus | SC(AT)sk SC(AT)ss SC(AT)us | ITsk ITss ITus | SC(IT)sk SC(IT)ss SC(IT)us | PTsk PTss PTus | SC(PT)sk SC(PT)ss SC(PT)us |
Total | STMix | SPMix | ST(AO)Mix | SC(AO)Mix | ST(AI)Mix | SC(AI)Mix | ATMix | ARMix | ACMix | SC(AT)Mix | ITMix | SC(IT)Mix | PTMix | SC(PT)Mix |
Output | SO | SO(AO) | SO(AI) | 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.
1. | (AO) | = |
|
2. | ST(AO) | = | ST ×
|
3. SC(AO) = ST(AO) × SR
4. SO(AO) = AO
5. | (AI) | = |
| ||
= |
|
6. | ST(AI) | = | ST ×
|
7. SC(AI) = ST(AI) × SR
8. | SO(AI) | = | SO ×
| ||
= | SO × 1.16 |
9. SC(AT) = AT × SR
10. SC(IT) = IT × SR
11. PT = AT − IT
12. SC(PT) = PT × SR
Wish not to recalculate standards
In the formulae, use the adjustment factorsAO |
SO |
AI |
SI |
Additionally using T × R for C in the formulae may eliminate the need to build the cost column in the working table.
Formulae that can be used in all cases
Labor/Labour | |||||
LCV LRPV LUV/LGEV LEV LITV LMV/GCV LYV/LSEV | = = = = = = = | SC(AO) SC(AT) SC(AO) SC(AO) SC(AI) SC(AO) | − − − − − − | AC AC SC(AT) SC(PT) SC(IT) SC(PT) SC(AI) | Cost Variance Rate of Pay Variance Usage/Gross-Efficiency Variance Efficiency Variance Idle Time Variance Mix/Gang-Composition Variance Yield/Sub-Efficiency Variance |
We can derive all other forms of the formulae from these.
- Keeping the suffix attached to quantity, replace
- SC with ST × SR
- AC with AT × AR
Eg : SC(AO) − AC, gives ST(AO) × SR − AT × AR
- To use formulae without having to recalculate standards, additionally replace
- (AO) with ×
AO SO - (AI) with ×
AI SI - (AT) with ×
(whereby SC(AT) gives AT × SR)AT ST - (PT) with ×
(whereby SC(PT) gives PT × SR)PT ST - (IT) with ×
(whereby SC(IT) gives IT × SR)IT ST
ST(AO) × SR, gives ST ×
× SRAO SO - (AO) with ×
Formulae containing the expression AT × SR or PT × SR or IT × SR should not be used for calculating the variance for the mix (total) in case where there are two or more labour/labor types being used.
Problem
During a 2 week period the actual production data revealed that there were 28 men, 20 women and 35 boys working in the gang and were paid @ 6, 3 and 3 per hour respectively. In achieving an output of 10,200 units, the average weekly work hours were 42.
There was a breakdown of power and no work was possible for 5 hours on a day. However, during this time the boys had been working as their work does not need power.
Calculate all possible variances relating to labour/labor.
Working Notes - Working Table
Calculation of work times
Particulars | Men | Women | Boys | Total |
---|---|---|---|---|
Standard/Budgeted (a) Number Working (b) Weekly Work Time (in hrs) Total Weekly Work Time (in hrs) (a) × (b) Output | 25 40 1,000 | 20 40 800 | 40 40 1,600 | 3,400 5,000 |
Actual (c) Number Working (d) Weekly Work Time (in hrs) (e) Number of Weeks Working (f) Time Lost (on a day) (in hrs) Total (g) Work Time (in hrs) (c) × (d) × (e) (h) Idle Time (c) × (f) (i) Productive Time (g) − (h) Output | 28 42 2 5 2,352 140 2,212 | 20 42 2 5 1,680 100 1,580 | 35 42 2 0 2,940 0 2,940 | 6,972 240 6,732 10,200 |
Working Table
Working table incorporating the data in the problem and the calculated values including recalculated standardsStandard | Actual | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
for SO | for AO | for AI | Total | Idle (Abnormal) | Productive | |||||||||
ST | SR | ST(AO) | SC(AO) | ST(AI) | SC(AI) | AT | AR | AC | SC(AT) | IT | SC(IT) | PT | SC(PT) | |
Factor | 2.04 | 1.98 | ||||||||||||
Men Women Boys | 1,000 800 1,600 | 5 4 3 | 2,040 1,632 3,264 | 10,200 6,528 9,792 | 1,980 1,584 3,168 | 9,900 6,336 9,504 | 2,352 1,680 2,940 | 6 3 3 | 14,112 5,040 8,820 | 11,760 6,720 8,820 | 140 100 0 | 700 400 0 | 2,212 1,580 2,940 | 11,060 6,320 8,820 |
Total | 3,400 | 6,936 | 26,520 | 6,732 | 25,740 | 6,972 | 27,972 | 27,300 | 240 | 1,100 | 6,732 | 26,200 | ||
Output | 5,000 SO | 10,200 SO(AO) | 9,900 SO(AI) | 10,200 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.
1. | (AO) | = |
| ||
= |
| ||||
= | 2.04 |
2. | ST(AO) | = | ST ×
| ||
= | ST × 2.04 |
3. SC(AO) = ST(AO) × SR
4. SO(AO) = AO
5. | (AI) | = |
| ||
= |
| ||||
= |
| ||||
= | 1.98 |
6. | ST(AI) | = | ST ×
| ||
= | ST × 1.98 |
7. SC(AI) = ST(AI) × SR
8. | SO(AI) | = | SO ×
| ||
= | SO × 1.98 |
9. SC(AT) = AT × SR
10. SC(IT) = IT × SR
11. PT = PT − IT
12. SC(PT) = PT × SR
13. | SC/UO | = |
| ||
= |
| ||||
= | 2.6/unit |
Illustration - Solution
Labor/Labour Cost Variance ~ LCV
LCV = SC(AO) − AC
Labor/Labour Cost Variance due to
Men, | ||||
LCVm | = | SC(AO)m − ACm | ||
= | 10,200 − 14,112 | = | − 3,912 [Adv] | |
Women, | ||||
LCVw | = | SC(AO)w − ACw | ||
= | 6,528 − 5,040 | = | + 1,488 [Fav] | |
Boys, | ||||
LCVb | = | SC(AO)b − ACb | ||
= | 9,792 − 8,820 | = | + 972 [Fav] | |
TLCV or LCVMix | = | − 1,452 [Adv] | ||
Labor/Labour Mix, | ||||
LCVMix | = | SC(AO)Mix − ACMix | ||
= | 26,520 − 27,972 | = | − 1,452 [Adv] |
Labor/Labour Rate of Pay Variance ~ LRPV
LRPV = SC(AT) − AC
Labor/Labour Rate of Pay Variance due to
Men, | ||||
LRPVm | = | SC(AT)m − ACm | ||
= | 11,760 − 14,112 | = | − 2,352 [Adv] | |
Women, | ||||
LRPVw | = | SC(AT)w − ACw | ||
= | 6,720 − 5,040 | = | + 1,680 [Fav] | |
Boys, | ||||
LRPVb | = | SC(AT)b − ACb | ||
= | 8,820 − 8,820 | = | 0 | |
TLRPV | = | − 672 [Adv] | ||
Labor/Labour Mix, | ||||
LRPVMix | = | SC(AT)Mix − ACMix | ||
= | 27,300 − 27,972 | = | − 672 [Adv] |
Labor/Labour Usage/Gross-Efficiency Variance ~ LUV/LGEV
LUV/LGEV = SC(AO) − SC(AT)
Labor/Labour Efficiency Variance due to
Men, | ||||
LUV/LGEVm | = | SC(AO)m − SC(AT)m | ||
= | 10,200 − 11,760 | = | − 1,560 [Adv] | |
Women, | ||||
LUV/LGEVw | = | SC(AO)w − SC(AT)w | ||
= | 6,528 − 6,720 | = | − 192 [Adv] | |
Boys, | ||||
LUV/LGEVb | = | SC(AO)w − SC(AT)w | ||
= | 9,792 − 8,820 | = | + 972 [Fav] | |
TLGUV/TLGEV | = | − 780 [Adv] | ||
Labor/Labour Mix, | ||||
LUV/LGEVMix | = | SC(AO)Mix − SC(AT)Mix | ||
= | 26,520 − 27,300 | = | − 780 [Adv] |
Labor/Labour Efficiency Variance ~ LEV
LEV = SC(AO) − SC(PT)
Labor/Labour Efficiency Variance due to
Men, | ||||
LEVm | = | SC(AO)m − SC(PT)m | ||
= | 10,200 − 11,060 | = | − 860 [Adv] | |
Women, | ||||
LEVw | = | SC(AO)w − SC(PT)w | ||
= | 6,528 − 6,320 | = | + 208 [Fav] | |
Boys, | ||||
LEVb | = | SC(AO)w − SC(PT)w | ||
= | 9,792 − 8,820 | = | + 972 [Fav] | |
TLUV/TLEV | = | + 320 [Fav] | ||
Labor/Labour Mix, | ||||
LEVMix | = | SC(AO)Mix − SC(PT)Mix | ||
= | 26,520 − 26,200 | = | + 320 [Fav] |
Labor/Labour Idle Time Variance ~ LITV
LITV = − SC(IT)
Labor/Labour Idle Time Variance due to
Men, | ||||
LITVm | = | − SC(IT)m | = | − 700 [Adv] |
Women, | ||||
LEVw | = | − SC(IT)w | = | − 400 [Adv] |
Boys, | ||||
LITVb | = | − SC(IT)w | = | 0 |
TITV | = | − 1,100 [Adv] | ||
Labor/Labour Mix, | ||||
LITVMix | = | − SC(IT)Mix | = | − 1,100 [Adv] |
Labor/Labour Mix/Gang-Composition Variance ~ LMV/GCV
LMV/GCV = SC(AI) − SC(PT)
Labor/Labour Mix/Gang-Composition Variance due to
Men, | ||||
LMV/GCVm | = | SC(AI)m − SC(PT)m | ||
= | 9,900 − 11,060 | = | − 1,160 [Adv] | |
Women, | ||||
LMV/GCVw | = | SC(AI)w − SC(PT)w | ||
= | 6,336 − 6,320 | = | + 16 [Fav] | |
Boys, | ||||
LMV/GCVb | = | SC(AI)b − SC(PT)b | ||
= | 9,504 − 8,820 | = | + 684 [Fav] | |
TLMV/TGCV | = | − 460 [Adv] | ||
LMV/GCVMix | = | SC(AI)Mix − SC(PT)Mix | ||
= | 25,740 − 26,200 | = | − 460 [Adv] |
Labor/Labour Yield/Sub-Efficiency Variance ~ LYV/LSEV
LYV/LSEV = SC(AO) − SC(AI)
Labor/Labour Yield/Sub-Efficiency Variance due to
Men, | ||||
LYV/LSEVm | = | SC(AO)m − SC(AI)m | ||
= | 10,200 − 9,900 | = | + 300 [Fav] | |
Women, | ||||
LYV/LSEVw | = | SC(AO)w − SC(AI)w | ||
= | 6,528 − 6,336 | = | + 192 [Fav] | |
Boys, | ||||
LYV/LSEVb | = | SC(AO)b − SC(AI)b | ||
= | 9,792 − 9,504 | = | + 288 [Fav] | |
TLYV/TLSUV/TLSEV | = | + 780 [Fav] | ||
Labor/Labour Mix, | ||||
LYV/LSEVMix | = | SC(AO)Mix − SC(AI)Mix | ||
= | 26,500 − 25,740 | = | + 780 [Fav] |
Solution (minimal detail)
Labor/Labour Cost Variance
LCV = SC(AO) − AC
Men, Women, Boys, | 10,200 − 14,112 6,528 − 5,040 9,792 − 8,820 | = = = | − 3,912 [Adv] + 1,488 [Fav] + 972 [Fav] |
Mix/Total, | 26,520 − 27,972 | = | − 1,452 [Adv] |
Labor/Labour Rate of Pay Variance
LRPV = SC(AT) − AC
Men, Women, Boys, | 11,760 − 14,112 6,720 − 5,040 8,820 − 8,820 | = = = | − 2,352 [Adv] + 1,680 [Fav] 0 |
Mix/Total, | 27,300 − 27,972 | = | − 672 [Adv] |
Labor/Labour Usage/Gross-Efficiency Variance
LUV/LGEV = SC(AO) − SC(AT)
Men, Women, Boys, | 10,200 − 11,760 6,528 − 6,720 9,792 − 8,820 | = = = | − 1,560 [Adv] − 192 [Adv] + 972 [Fav] |
Mix/Total, | 26,520 − 27,300 | = | − 780 [Adv] |
Labor/Labour Efficiency Variance
LEV = SC(AO) − SC(PT)
Men, Women, Boys, | 10,200 − 11,060 6,528 − 6,320 9,792 − 8,820 | = = = | − 860 [Adv] + 208 [Fav] + 972 [Fav] |
Mix/Total, | 26,520 − 26,200 | = | + 320 [Fav] |
Labor/Labour Idle Time Variance
LITV = − SC(IT)
Men, Women, Boys, | = = = | − 700 [Adv] − 400 [Adv] 0 | |
Mix/Total, | = | − 1,100 [Adv] |
Labor/Labour Mix/Gang-Composition Variance
LMV/GCV = SC(AI) − SC(PT)
Men, Women, Boys, | 9,900 − 11,060 6,336 − 6,320 9,504 − 8,820 | = = = | − 1,160 [Adv] + 16 [Fav] + 684 [Fav] |
Mix/Total, | 25,740 − 26,200 | = | − 460 [Adv] |
Labor/Labour Yield/Sub-Efficiency Variance
LYV/LSEV = SC(AO) − SC(AI)
Men, Women, Boys, | 10,200 − 9,900 6,528 − 6,336 9,504 − 8,820 | = = = | + 300 [Fav] + 192 [Fav] + 288 [Fav] |
Mix/Total, | 26,500 − 25,740 | = | + 780 [Fav] |
Solution (alternative presentation)
Men | Women | Boys | Mix/Total | |
---|---|---|---|---|
LYV/LSEV Men Women Boys Mix SC(AO) 10,200 6,528 9,792 26,500 − − − − − SC(AI) 9,900 6,336 9,504 25,740 Men Women Boys Mix SC(AI) 9,900 6,336 9,504 25,740 − − − − − SC(PT) 11,060 6,320 8,820 26,200 | + 300 − 1,160 | + 192 + 16 | + 288 + 684 | + 780 − 460 |
LEV Men Women Boys Mix SC(AO) 10,200 6,528 9,792 26,520 − − − − − SC(PT) 11,060 6,320 8,820 26,200 Men Women Boys Mix − SC(IT) | − 860 − 700 | + 208 − 400 | + 972 0 | + 320 − 1,100 |
LUV/LGEV Men Women Boys Mix SC(AO) 10,200 6,528 9,792 26,520 − − − − − SC(AT) 11,760 6,720 8,820 27,300 Men Women Boys Mix SC(AT) 11,760 6,720 8,820 27,300 − − − − − AC 14,112 5,040 8,820 27,972 | − 1,560 − 2,352 | − 192 + 1,680 | + 972 0 | − 780 − 672 |
LCV Men Women Boys Mix SC(AO) 10,200 6,528 9,792 26,520 − − − − − AC 14,112 5,040 8,820 27,972 | − 3,912 | + 1,488 | + 972 | − 1,452 |
Verification
Formula | Men | Women | Boys | Mix/Total | |
---|---|---|---|---|---|
LYV/LSEV + LMV/GCV | SC(AO) − SC(AI) SC(AI) − SC(PT) | + 300 − 1,160 | + 192 + 16 | + 288 + 684 | + 780 − 460 |
LEV + LITV | SC(AO) − SC(PT) − SC(IT) | − 860 − 700 | + 208 − 400 | + 972 0 | + 320 − 1,100 |
LUV/LGEV + LRPV | SC(AO) − SC(AT) SC(AT) − AC | − 1,560 − 2,352 | − 192 + 1,680 | + 972 0 | − 780 − 672 |
LCV | SC(AO) − AC | − 3,912 | + 1,488 | + 972 | − 1,452 |
Simplest
One may use this as the simplest presentation of calculations, since all the amounts used in the formula are present in the working table.If it is for verification purposes, we may avoid the formula column.
Adopt a presentation based on the examination you are attending and the proportion of marks allotted and time available to/for the problem.