# Labour/Labor Cost Variance

# Illustration - Problem

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

⇒ Labour/Labor Cost Variance (**LCV**)

= | SC(AO) − ACStandard 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 ×
| ||

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

- ×

replaces the suffix (AO) in calculationsAO SO - 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

LCV_{Lab} | = | SC(AO)_{Lab} − AC_{Lab} |

Or | = | AO (SC/UO_{Lab} − AC/UO_{Lab}) |

## For all Labour/Labor types together

Total Labour/Labor Cost variance

TLCV | = | ΣLCV_{Lab}Sum of the variances measured for each labour/labor type separately |

Labour/Labor Cost variance for the Mix

LCV_{Mix} | = | SC(AO)_{Mix} − AC_{Mix} |

Or | = | AO (SC/UO_{Mix} − AC/UO_{Mix}) |

**TLCV = LCV _{Mix}**

# Illustration - Solution

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) | = |
| ||

= |
| ||||

= | 0.96 |

2. | ST(AO) | = | ST ×
| ||

= | 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, | ||||

LCV_{sk} | = | SC(AO)_{sk} − AC_{sk} | ||

= | 3,840 − 5,280 | = | − 1,440 [Adv] | |

Semi-Skilled Labour/Labor, | ||||

LCV_{ss} | = | SC(AO)_{ss} − AC_{ss} | ||

= | 5,760 − 7,000 | = | − 1,240 [Adv] | |

Unskilled Labour/Labor, | ||||

LCV_{us} | = | SC(AO)_{us} − AC_{us} | ||

= | 1,440 − 2,640 | = | − 1,200 [Adv] | |

TLCV or LCV_{Mix} | = | − 3,880 [Adv] | ||

Labour/Labor Mix, | ||||

LCV_{Mix} | = | SC(AO)_{Mix} − AC_{Mix} | ||

= | 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)

AO |

SO |

## 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

Unskilled200

400

15020

15

104,000

6,000

1,500240

500

22022

14

125,280

7,000

2,64020

36

34Total 750 11,500 960 14,920 90 Output 7,500

SO7,200

AO1. 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

Unskilled200

400

15020

15

10240

500

22022

14

1220

36

34Total 750 11,500 960 90 Output 7,500

SO7,200

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

## 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

## LCV

_{Lab}- SC(AO)
_{Lab}___ AC_{Lab}

## LCV

_{Mix}- SC(AO)
_{Mix}___ AC_{Mix}

The variance would be

- zero when =
- Positive when >
- Negative when <

### TLCV

Variance of Mix and Total Variance are the same.Variance

_{Mix}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- each labour/labor type variance being zero, or
- 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

- 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