# Labour/Labor Variances :: Formulae Review : Illustration

 Methodology » Approach

#### Arrange the data in a Working Table

Making a working table would form the first step for your problem solving effort.

True, your ability to solve problems on this topic is one way judged/decided by your ability to recollect the formulae. But, if you adopt the formulae that are capable of being used in all cases, it won't be difficult at all.

Yes, it would be very easy.

Your problem solving capability is limited by your ability to interpret the problem. If you notice all the examples we have given, the data in all the problems is structured (presented) in a similar manner, in the form of a table.

There lies the trick to make problem solving easy. Whatever may be the way the problem is presented (what we call problem models), get habituated to arranging the information in the form of a table as given below. Once you arrange that information, it would be very easy for you. Recollect the relevant formula and apply it.

If you try to understand the logic behind each formula, recollecting them also would be very easy. That is the reason we recommend the student to use the formula that is capable of being used in all cases.

Working table for arranging your data.

Time(hrs) Rate(Rs/hr) Cost(Rs) Rate(Rs/hr) Total/Gross Abnromal Net Time(hrs) Cost(Rs) Time(hrs) Cost(Rs) Standard [Production: SO] Actual [Production: AO] Sk STSk SRSk SCSk ARSk AT(G)Sk AC(G)Sk AT(Id)Sk AC(Id)Sk AT(N)Sk AC(N)Sk Se STSe SRSe SCSe ARSe AT(G)Se AC(G)Se AT(Id)Se AC(Id)Se AT(N)Se AC(N)Se Un .. .. .. .. .. .. .. .. .. .. STMix SRMix SCMix ARMix AT(G)Mix AC(G)Mix AT(Id)Mix AC(Id)Mix AT(N)Mix AT(N)Mix

There are two approaches to solving problems.

• #### Using the given data as it is

If you use the formulae that are capable of being used in all situations, you just need to build the working table from the given data and things from thereon would be involving substituting data and evaluating the result.

This would be the best approach as all the adjustments you need to make with regard to the difference between the AO and SO as well as AT(N)Mix and STMix would be taken care of within the formulae itself.

• #### By Recalculating Standards where needed

If at all you wish to calculate variances by recalculating the standards, you have to recalculate the standards twice.
1. Once based on output (Standards for Actual Output) to ensure the condition SO = AO. The values for ST and SO for calculating LCV and LEV/LUV should be considered from the working table ensuring this condition is satisfied.
2. The Second time based on input (Standards for Actual Input) to ensure the condition AT(N)Mix = STMix. The values for ST and SO for calculating LMV/GCV and LYV/LSEV/LSUV should be considered from the working table ensuring this condition is satisfied.

All other values i.e. SR and the actual data (AR, AT, AO) are not influenced by these conditions i.e., they would be the same in all cases.

#### Recommended Formulae!!!

The formulae that can be used in all situations should be used so that you would get accustomed to the formulae after doing some problems and would not be worried about not being able to recollect the correct formula.

 Formulae that can be used in all cases

1. Labour/Labor Cost Variance

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

2. Labour/Labor Rate of pay Variance

 ⇒ LRPV = (ST − AT(G)) × AR

3. Labour/Labor (Gross) Efficiency/Usage Variance

⇒ LEV/LUV(G) =
({
 AO SO
× ST} − AT(G)) × SR

4. Labour/Labor (Net) Efficiency/Usage Variance

⇒ LEV/LUV(N) =
({
 AO SO
× ST} − AT(N)) × SR

5. Labour/Labor Idle Time Variance

 ⇒ LITV = − AT(Id) × SR

6. Labour/Labor Mix/Gang-Composition Variance

⇒ LMV/GCV = ({
 AT(N)Mix STMix
× ST } − AT) × SR

7. Labour/Labor Yield/Sub-Efficiency/Sub-Usage Variance

⇒ LYV/LSEV/LSUV =
(AO − ({
 AT(N)Mix STMix
× SO } × SR(SO) )

• Standard Rate of Output

SR(SO) =  SCMix SO

#### Where

1. ST = Standard Time of each Labour/Labor Type
2. SO = Standard Output
3. SR = Standard wage Rate for each Labour/Labor Type
4. STMix = Standard Time of Mix
5. SCMix = Standard Cost of Mix
6. SR(SO) = Standard Rate of Standard Output/Yield
7. AT(G) = Gross Actual Time of each Labour/Labor Type
8. AT(Id/Ab) = Abnormal Idle Time for each Labour/Labor Type
9. AT(N) = Net Actual Time for each Labour/Labor Type
10. AR = Actual Wage Rate for each Labour/Labor Type
11. AO = Actual Output
12. AT(G)Mix = Gross Actual Time of Mix
13. AT(Ab/Id)Mix = Abnormal Idle time in Actual Mix
14. AT(N)Mix = Net Actual Time of Mix

#### Note :

If you understand the concept behind the variance, remembering the formula would not poce a problem at all. You may use the following tips to aid your effort (we feel even this should not be necessary for an average student).
• Remember the simple formulae excluding the correction/adjustment factor in which case the formulae for LEV/LUV and LMV/GCV would be the same.
• The ST is to corrected/adjusted by a factor:
• AO/SO for calculating the LCV, LEV/LUV(G)and LEV/LUV(N)
• AT(N)Mix/STMix for calculating LMV/GCV and LYV/LSEV/LSUV
• The SO is to be corrected/adjusted by a factor
• AT(N)Mix/STMix for calculating LYV/LSEV/LSUV
LYV/LSEV/LSUV is dependent on "SO" and not "ST".
• #### Calculating Total Variances

Where there are two or more labour/labor types involved in the production process, total variances can be calculated as the sum of the variances for each labour/labor type calculated separately using the above formulae.

LYV/LSEV/LSUV cannot be calculated for each labour/labor type separately. Only TLYV/TLSEV/TLSUV can be calculated using the above formula.

TLCV variance can be calculated using a separate formula without requiring to calculate the individual variances.

 A Problem
 Three kinds of labourers/laborers Men, Women and Boys are required for the manufacture of a product. They are paid at the rate of Rs. 5 per hour, Rs. 4 per hour and Rs. 3 per hour respectively. The standards reveal that a gang of 25 men, 20 women and 40 boys are required to work for a time of 40 hrs over a week to bring out an output of 5,000 units. 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 @ Rs. 6, Rs. 3 and Rs. 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 realting to labour/labor.

 Working Notes » Working Table
Working Notes: Calculation of work times.

Particulars Men Women Boys Total
Standard/Budgeted
(a) Number Working 25 20 40
(b) Weekly Work Time [In hrs] 40 40 40
Total Weekly Work Time (in hrs) [(a) × (b)] 1,000 800 1,600 3,400
Actual
(c) Number Working 28 20 35
Actual [Gross/Total]
(d) Weekly Work Time [In hrs] 42 42 42
Total Work Time (in hrs) [(c) × (d)] 2,352 1,680 2,940 6,972
Actual [Abnormal/Idle]
(e) Abnormal Loss Time [in hrs] 5 5 0
Total Abnormal Loss Time (in hrs) [(c) × (e)] 140 100 0 240
Actual [Net]
[Actual [Total] − Actual [Abnormal]] [in hrs] 2,212 1,580 2,940 6,732

#### Working Table

Working table incorporating the data in the problem

Time(hrs) Rate(Rs/hr) Cost(Rs) Rate(Rs/hr) Total Normal Abnromal Time(hrs) Cost(Rs) Time(hrs) Cost(Rs) Standard [Production: 5,000 units] Actual [Production: 10,200 units] Men 1,000 5 5,000 6 2,352 14,112 2,212 13,272 140 840 Women 800 4 3,200 3 1,680 5,040 1,580 4,740 100 300 Boys 1,600 3 4,800 3 2,940 8,820 2,940 8,820 3,400 13,000 6,972 27,972 6,732 26,832 240 1,140

SR(SO) =
 SCMix SO
⇒ SR(SO) =
 Rs. 13,000 5,000 units
⇒ SR(SO) = Rs. 2.60/unit

 The Solution

#### • Labour/Labor Cost Variance [LCV]

LCV = ({
 AO SO
× ST } × SR ) − (AT(G) × AR)
Using, LCVLab = ({
 AO SO
× STLab } × SRLab ) − (AT(G)Lab × ARLab)

Labour/Labor Cost Variance due to labourers/laborers who are
Men =
({
 10,200 units 5,000 units
× 1,000 hrs } × Rs. 5/hr ) − (2,352 hrs × Rs. 6/hr)
= (2.04 × 1,000 hrs × Rs. 5/hr) − (Rs. 14,112)
= Rs. 10,200 − Rs. 14,112
= − Rs. 3,912 ⇒ LCVM = − Rs. 3,912 [Adv]
Women =
({
 10,200 units 5,000 units
× 800 hrs } × Rs. 4/hr ) − (1,680 hrs × Rs. 3/hr)
= (2.04 × 800 hrs × Rs. 4/hr) − (Rs. 5,040)
= Rs. 6,528 − Rs. 5,040
= + Rs. 1,488 ⇒ LCVW = + Rs. 1,488 [Pos]
Boys =
({
 10,200 units 5,000 units
× 1,600 hrs } × Rs. 3/hr ) − (2,940 hrs × Rs. 3/hr)
= (2.04 × 1,600 hrs × Rs. 3/hr) − (Rs. 8,820)
= Rs. 9,792 − Rs. 8,820
= + Rs. 972 ⇒ LCVB = + Rs. 972 [Pos]
Total Labour/Labor Cost Variance ⇒ TLCV = − Rs. 1,452 [Adv]

#### • Labour/Labor Rate of Pay Variance [LRPV]

LRPV = ATG × (SR − AR)

Using, LRPV = AT(G)Lab × (SRLab − ARLab)

Labour/Labor Rate of Pay Variance due to labourers/laborers who are
 • Men = 2,352 hrs (Rs. 5/hr − Rs. 6/hr = 2,352 hrs (− Rs. 1/hr) = − Rs. 2,352 ⇒ LRPVM = − Rs. 2,352 [Adv] • Women = 1,680 hrs (Rs. 4/hr − Rs. 3/hr) = 1,680 hrs (+ Rs. 1/hr) = + Rs. 1,680 ⇒ LRPVW = + Rs. 1,680 [Fav] • Boys = 2,940 hrs (Rs. 3/hr − Rs. 3/hr) = 2,940 hrs (0) = 0 ⇒ LRPVB = Nil [None] Total Rate of Pay Variance ⇒ TLRPV = + Rs. 672 [Fav]

#### • Labour/Labor (Gross) Efficiency/Usage Variance [LEV/LUV(G)]

LEV/LUV(N) =
({
 AO SO
× ST} − ATG) × SR
Using, LEV/LUV(N)Lab =
({
 AO SO
× STLab} − AT(G)Lab) × SRLab

Labour/Labor Efficiency/Usage Variance due to the labourers/laborers who are
Men =
({
 10,200 units 5,000 units
× 1,000 hrs − 2,352 hrs) × Rs. 5/hr}
= ({2.04 × 1,000 hrs} − 2,352 hrs) × Rs. 5/hr
= ({2,040 hrs − 2,352 hrs) × Rs. 5/hr
= (− 312 hrs) × Rs. 5/hr
= − Rs. 1,560 ⇒ LEV/LUV(G)M = − Rs. 1,560 [Adv]
Women =
({
 10,200 units 5,000 units
× 800 hrs − 1,680 hrs) × Rs. 4/hr}
= ({2.04 × 800 hrs} − 1,680 hrs) × Rs. 4/hr
= ({1,632 hrs − 1,680 hrs) × Rs. 4/hr
= (− 48 hrs) × Rs. 4/hr
= − Rs. 192 ⇒ LEV/LUV(G)W = − Rs. 192 [Adv]
Boys =
({
 10,200 units 5,000 units
× 1,600 hrs − 2,940 hrs) × Rs. 3/hr}
= ({2.04 × 1,600 hrs} − 2,940 hrs) × Rs. 3/hr
= ({3,264 hrs − 2,940 hrs) × Rs. 3/hr
= (+ 324 hrs) × Rs. 3/hr
= + Rs. 972 ⇒ LEV/LUV(G)B = + Rs. 972 [Fav]
Total Labour/Labor Efficiency/Usage Variance ⇒ TLEV/TLUV(G) = − 780 [Adv]

#### • Labour/Labor (Net) Efficiency/Usage Variance [LEV/LUV(N)]

LEV/LUV(N) =
({
 AO SO
× ST} − ATN) × SR
Using, LEV/LUV(N)Lab =
({
 AO SO
× STLab} − AT(N)Lab) × SRLab

Labour/Labor Efficiency/Usage Variance due to the labourers/laborers who are
Men =
({
 10,200 units 5,000 units
× 1,000 hrs − 2,212 hrs) × Rs. 5/hr}
= ({2.04 × 1,000 hrs} − 2,212 hrs) × Rs. 5/hr
= ({2,040 hrs − 2,212 hrs) × Rs. 5/hr
= (− 172 hrs) × Rs. 5/hr
= − Rs. 860 ⇒ LEV/LUV(N)M = − Rs. 860 [Adv]
Women =
({
 10,200 units 5,000 units
× 800 hrs − 1,580 hrs) × Rs. 4/hr}
= ({2.04 × 800 hrs} − 1,580 hrs) × Rs. 4/hr
= ({1,632 hrs − 1,580 hrs) × Rs. 4/hr
= (+ 52 hrs) × Rs. 4/hr
= + Rs. 208 ⇒ LEV/LUV(N)W = + Rs. 208 [Fav]
Boys =
({
 10,200 units 5,000 units
× 1,600 hrs − 2,940 hrs) × Rs. 3/hr}
= ({2.04 × 1,600 hrs} − 2,940 hrs) × Rs. 3/hr
= ({3,264 hrs − 2,940 hrs) × Rs. 3/hr
= (+ 324 hrs) × Rs. 3/hr
= + Rs. 972 ⇒ LEV/LUV(N)B = + Rs. 972 [Fav]
Total Labour/Labor Efficiency/Usage Variance ⇒ TLEV/TLUV(N) = + Rs. 320 [Fav]

#### • Labour/Labor Idle Time Variance [LITV]

LITV = − (AT(Id) × SR)

Using, LITV = − (AT(Id)Lab × SRLab)

Labour/Labor Idle Time Variance due to labour/labor types who are
 • Men = − (140 hrs × Rs. 5/hr) = − Rs. 700 ⇒ LITVM = − Rs. 700 [Adv] • Women = − (100 hrs × Rs. 4/hr) = − Rs. 400 ⇒ LITVW = − Rs. 400 [Adv] • Boys = − (0 hrs × Rs. 3/hr) = 0 ⇒ LITVB = Nil [None] Total Labour/Labor Idle Time Variance ⇒ TLITV = − Rs. 1,100 [Adv]

#### • Labour/Labor Mix/Gang-Composition Variance [LMV/GCV]

LMV/GCV =
({
 AT(N)Mix STMix
× ST} − AT(N)) × SR

Using, LMV/GCVLab =
({
 AT(N)Mix STMix
× STLab} − AT(N)Lab) × SRLab

Labour/Labor Mix or Gang Composition Variance due to labourers/laborers who are
Men =
({
 6,732 hrs 3,400 hrs
× 1,000 hrs} − 2,212 hrs) × Rs. 5/hr
= ({1.98 × 1,000 hrs) − 2,212 hrs) × Rs. 5/hr
= (1,980 hrs − 2,212 hrs) × Rs. 5/hr
= (− 232 hrs) × Rs. 5/hr
= − Rs. 1,160 ⇒ LMV/GCVM = − Rs. 1,160 [Adv]
Women =
({
 6,732 hrs 3,400 hrs
× 800 hrs} − 1,580 hrs) × Rs. 4/hr
= ({1.98 × 800 hrs) − 1,580 hrs) × Rs. 4/hr
= (1,584 hrs − 1,580 hrs) × Rs. 4/hr
= (+ 4 hrs) × Rs. 4/hr
= + Rs. 16 ⇒ LMV/GCVW = + Rs. 16 [Fav]
Boys =
({
 6,732 hrs 3,400 hrs
× 1,600 hrs}
− 2,940 hrs) × Rs. 3/hr
= ({1.98 × 1,600 hrs) − 2,940 hrs) × Rs. 3/hr
= (3,168 hrs − 2,940 hrs) × Rs. 3/hr
= (+ 228 hrs) × Rs. 3/hr
= + Rs. 684 ⇒ LMV/GCVB = + Rs. 684 [Fav]
Total Labour Mix or Gang Composition Variance ⇒ TLMV/TGCV = − Rs. 460 [Adv]

#### • Labour/Labor Yield/Sub-Efficiency/Sub-Usage Variance [LYV/LSEV/LSUV]

TLYV =
(AO − {
 AT(N)Mix STMix
× SO} ) × SR(SO)
Therefore, total labour/labor yield Variance,
⇒ TLYV/TLSEV/TLSUV =
(10,200 units − {
 6,732 hrs 3,400 hrs
× 5,000 units} ) × Rs. 2.60/unit
= (10,200 units − {1.98 × 5,000 units} ) × Rs. 2.60/unit
= (10,200 units − 9,900 units) × Rs. 2.60/unit
= (+ 300 units) × Rs. 2.60/unit
= + Rs. 780 [Pos or Fav]

 Verification

 TLEV/TLUV(N) + TLITV = (+ 320) + (− Rs. 1,100) = (− 780) = TLEV/TLUV(G) → TRUE

 TLRPV + TLEV/TLUV(N) + TLITV = (− Rs. 672) + (+ 320) + (− Rs. 1,100) = (− 1,452) = TLCV → TRUE

 TLMV/TGCV + TLYV/TLSEV/TLSUV = (− Rs. 460) + (+ Rs. 780) = (+ Rs. 320) = TLUV/TLSEV(N) → TRUE
 TLRPV + TLMV/TGCV + TLYV/TLSEV/TLSUV(N) + TLITV = (− Rs. 672) + (− Rs. 460) + (+ 780) + (− 1,100) = (− 1,452) = TLCV → TRUE

#### Wish to avoid approximation errors!!!

Consider as many places after the decimal as possible. The more places you consider, the lesser would be chance for error. This should not make you go crazily writing down numbers with long digits after the decimal. It would not be needed. One another method is to use fractions without writing them down in their decimal form, till you arrive at the last step. Say use Rs. 115/9 in place of Rs. 12.78 which would reduce the need for approximation to the greatest possible extent.

#### Caution

How does an amount of Rs. 123.45398723992873623212983439272 (Or) Rs. 143/7 sound......

Please, don't write your final figures as fractions or with more than two digits after the decimal. We are not in the science lab. We are talking of money.

 Author Credit : The Edifier ... Continued Page L:13