# Labour/Labor - Rate of Pay 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 - Labor/Labour Rate of Pay Variance ~ LRPV

It is the variance between the standard cost of actual time and the actual cost of labour/labor.

⇒ Labour/Labor Rate of Pay Variance (**LRPV**)

= | SC(AT) − ACStandard Cost of Actual Time − Actual Cost |

## Standard Cost of Actual Time

SC(AT) | = | AT × SR |

## Actual Cost

Based on inputs | ||

AC | = | AT × AR |

Based on output | ||

= | AO × AC/UO |

## Formula in useful forms

LRPV | = | SC(AT) − AC Standard Cost of Actual Time − Actual Cost |

Or | = | AT × (SR − AR) Actual Time × Difference between standard and actual rates |

## For each Labour/Labor type separately

Labour/Labor Rate of Pay variance for a Labour/Labor typeLRPV_{Lab} | = | SC(AT)_{Lab} − AC_{Lab} |

Or | = | AT_{Lab} × (SR_{Lab} − AP_{Lab}) |

## For all Labour/Labor types together

Total Labour/Labor Rate of Pay variance

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

Labour/Labor Rate of Pay Variance for the mix

LRPV_{Mix} | = | SC(AT)_{Mix} − AC_{Mix} |

= | AT_{Mix} × (SR_{Mix} − AP_{Mix}) [Conditional] This formula can be used for the mix only when the actual times mix ratio is the same as the standard time mix ratio. |

**TLRPV = LRPV _{Mix}**, when LRPV

_{Mix}exists.

## The Math

The variance in total cost is on account of two factors price and quantity.Consider the relation, Value (V) = Time (T) × Rate (R).

If T is constant, V = TR

⇒ V_{1} = T × R_{1} → (1)

⇒ V_{2} = T × R_{2} → (2)

(1) − (2)

⇒ V_{1} − V_{2} = T × R_{1} − T × R_{2}

⇒ V_{1} − V_{2} = T × (R_{1} − R_{2})

⇒ ΔV = T × ΔR, where T is a constant

⇒ ΔV ∞ ΔR

Change in value varies as change in rate

By taking both times at actual we are eliminating the effect of difference between the standard time and actual time, thereby leaving only the difference between rates.

# Recalculating Standards does not effect LRPV Calculations

The data used for calculating Labour/Labor Rate of Pay Variance, SR, AR, AT does not change on standards being recalculated either based on the output or input.

Standard | Actual | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

for SO | for AO | for AI | Total | Idle | Productive | |||||||

ST | SR | ST(AO) | SC(AO) | ST(AI) | SC(AI) | AT | AR | AC | SC(AT) | IT | PT | |

Factor | 0.96 | 1.16 | ||||||||||

Skilled Semi-Skilled Unskilled | 200 400 150 | 20 15 10 | 192 384 144 | 3,840 5,760 1,440 | 232 464 174 | 4,640 6,960 1,740 | 240 500 220 | 22 14 12 | 5,280 7,000 2,640 | 4,800 7,500 2,200 | 20 36 34 | 220 464 186 |

Total | 750 | 720 | 11,040 | 870 | 13,340 | 960 | 14,920 | 14,500 | 90 | 870 | ||

Output | 7,500 SO | 7,200 SO(AO) | 8,700 SO(AI) | 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.

(AO) | = |
| ||

= |
| |||

= | 0.96 |

(AI) | = |
| ||

= |
| |||

= |
| |||

= | 1.16 |

1. | ST(AO) | = | ST ×
| ||

= | ST × 0.96 |

2. SC(AO) = ST(AO) × SR

3. SO(AO) = AO

4. | ST(AI) | = | ST ×
| ||

= | ST × 1.16 |

5. SC(AI) = ST(AI) × SR

6. | SO(AI) | = | SO ×
| ||

= | SO × 1.16 |

7. AC = AT × AR

8. SC(AT) = AT × SR

# Illustration - Solution

**LRPV = SC(AT) − AC**

Labour/Labor Rate of Pay Variance due to

Skilled Labour/Labor, | ||||

LRPV_{sk} | = | SC(AT)_{sk} − AC_{sk} | ||

= | 4,800 − 5,280 | = | − 480 [Adv] | |

Semi Skilled Labour/Labor, | ||||

LRPV_{ss} | = | SC(AT)_{ss} − AC_{ss} | ||

= | 7,500 − 7,000 | = | + 500 [Fav] | |

Unskilled Labour/Labor, | ||||

LRPV_{us} | = | SC(AT)_{us} − AC_{us} | ||

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

TLRPV | = | − 420 [Adv] | ||

Labour/Labor Mix, | ||||

LRPV_{Mix} | = | SC(AT)_{Mix} − AC_{Mix} | ||

= | 14,500 − 14,920 | = | − 420 [Fav] |

# Illustration - Solution (alternative)

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 |

**LRPV = AT (SR − AR)**

Labour/Labor Rate of Pay Variance due to

Skilled Labour/Labor, | ||||

LRPV_{sk} | = | AT_{sk}(SR_{sk} − AR_{sk}) | ||

= | 240 hrs (20/hr − 22/hr) | |||

= | 240 hrs (− 2/hr) | = | − 480 [Adv] | |

Semi Skilled Labour/Labor, | ||||

LRPV_{ss} | = | AT_{ss}(SR_{ss} − AR_{ss}) | ||

= | 500 hrs (15/hr − 14/hr) | |||

= | 500 hrs (1/hr) | = | + 500 [Fav] | |

Unskilled Labour/Labor, | ||||

LRPV_{us} | = | AT_{us}(SR_{us} − AR_{us}) | ||

= | 220 hrs (10/hr − 12/hr) | |||

= | 220 hrs (− 2/hr) | = | − 440 [Adv] | |

TLRPV | = | − 420 [Adv] |

Standard Time Mix Ratio

STMR | = | ST_{sk} : ST_{ss} : ST_{us} |

= | 200 hrs : 400 hrs : 150 hrs | |

= | 4 : 8 : 3 |

Actual Time Mix Ratio

ATMR | = | AT_{sk} : AT_{ss} : AT_{us} |

= | 240 hrs : 500 hrs : 200 hrs | |

= | 12 : 25 : 10 |

Since this formula involves the term AT × SR and STMR ≠ ATMR, it cannot be used for calculating the variance for the mix.

# LRPV - Miscellaneous Aspects

## Actual Time

In all cases whether or not there is idle time loss, Actual time in the formula implies the total Actual Time and not just Productive time.The variance being measured is for the variance on account of the wage rate paid or payable. Since all time has to be paid for whether or not the time has been utilised, actual time here means the total time.

## Nature of Variance

Based on the relations derived from the formulae for calculating LRPV, we can identify the nature of Variance

- SC(AT) ___ AC
- SR ___ AR

## LRPV

_{Lab}- SC(AT)
_{Lab}___ AC_{Lab} - SR
_{Lab}___ AR_{Lab}

## LRPV

_{Mix}- SC(AT)
_{Mix}___ AC_{Mix} - SR
_{Mix}___ AR_{Mix}(conditional)only when STMR = ATMR.

The variance would be

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

### TLRPV

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.Sometimes, it may not be possible to calculate this figure using the formula used for calculating individual variances like when the formula contains the term AT × SR.

## Interpretation of the Variance

For each labour/labor type, for the actual time paid/payable for

Variance Rate paid/payable 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 individual variances and as such reflects their net effect.

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 this variance is on account of the actual rate paid/payable being more or less than the standard, the people or department responsible for deciding on the labour/labor rates to be paid can be held responsible for this variance.

# Formulae using Inter-relationships among Variances

- LRPV = LCV − LUV/LGEV
- LRPV = LCV − LEV − LITV
- LRPV = LCV − LMV/GCV − LYV/LSEV − 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 | — − 480 | — + 500 | — − 440 | — − 420 |

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