Calculate Labor/Labour Variances.

Working table populated with the information that can be obtained as it is from the problem data

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.

It is the difference between the standard cost for actual output and the standard cost of actual labour/labor time.

⇒ Labour/Labor Usage/Gross-Efficiency Variance (LUV/LGEV)

Standard Cost for Actual Output

Standard Cost of Actual Time

Formula in useful forms

Note

• ×

  AO

  SO

  replaces the suffix (AO) in calculations
• Finding the costs by building up the working table and using the formula involving costs is the simplest way to find variances.
• The formula involving costs can be used to find the Labour/Labor Usage/Gross-Efficiency Variance for individual labour/labor types as well as the mix of labour/labor types. Appropriate suffix _Lab or _Mix is used in the formula as an indicator.

For each Labour/Labor type separately

Labour/Labor Usage/Gross-Efficiency variance for a labour/labor type

For all Labour/Labor types together

Total Labour/Labor Usage/Gross-Efficiency Variance

Labour/Labor Usage/Gross-Efficiency variance for the Mix

TLUV/TLGEV = LEV/LGUV_Mix

The Math

Consider the relation, Value (V) = Time (T) × Price (R).

If R is constant, V = TR

⇒ V₁ = T₁ × R → (1)
⇒ V₂ = T₂ × R → (2)

(1) − (2)

⇒ V₁ − V₂ = T₁ × R − T₂ × R
⇒ V₁ − V₂ = (T₁ − T₂) × R
⇒ ΔV = ΔT × R, where R is a constant
⇒ ΔV ∞ ΔT

Change in value varies as change in time

By taking both rate of pays at standard we are eliminating the effect of difference between the standard rate of pay and actual rate of pay, thereby leaving only the difference between time usage.

3. SC(AO) = ST(AO) × SR

4. SC(AT) = AT × SR

5. SO(AO) = AO

LEV/LGUV = SC(AO) − SC(AT)

Labour/Labor Usage/Gross-Efficiency Variance due to

Alternative

• Calculating Costs in a working table

  Calculate SC and SC(AT) based on the given data in a working table and then use formulae based on costs.

  	Standard			Actual
  	for SO			Total				Idle
  	ST	SR	SC	AT	AR	AC	SC(AT)	IT
  Skilled Semi-Skilled Unskilled	200 400 150	20 15 10	4,000 6,000 1,500	240 500 220	22 14 12	5,280 7,000 2,640	4,800 7,500 2,200	20 36 34
  Total	750		11,500		960	14,920	14,500	90
  Output	7,500 SO			7,200 AO

  1. SC = ST × SR

  3. AC = AT × AR

  3. SC(AT) = AT × SR

  LUV/LGEV

  =

  SC × AO SO − SC(AT)

• Using Formula with Time and Rate

  Using the time and rate 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.

  	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

  LUV/LGEV = (ST ×

  AO

  SO

  − AT) × SR

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

Labour/Labor Idle Time variance represents a loss and is always a the value of a term and not a difference of two terms.

• Actual Time

  LUV/LGEV measures the variance in utilisation of total time paid for. Thus the time in this case means actual time.

• Nature of Variance

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

  • SC(AO) ___ SC(AT)
  • ST(AO) ___ AT

  LUV/LGEV_Lab

  • SC(AO)_Lab ___ SC(AT)_Lab
  • ST(AO)_Lab ___ AT_Lab

  LUV/LGEV_Mix

  • SC(AO)_Mix ___ SC(AT)_Mix
  • ST(AO)_Mix ___ AT_Mix (conditional)

    only when STMR = ATMR.

  The variance would be

  • zero when =
  • Positive when >
  • Negative when <

  TLUV/TLGEV

  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, for the output achieved

  Variance	Total Time input 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

  1. each labour/labor type variance being zero, or
  2. 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 labour/labor time used being more or less than the standard, the people or department responsible for production can be identified as the ones answerable for this variance.

  This conclusion would be appropriate when there is only one labour/labor type in use.

  When there are two or more labour/labor types

  When two or more labour/labor types are being used for the manufacture of a product, making only the people responsible for production answerable for the variance may not be appropriate as there would be three factors influencing the usage of labour/labor types.
  1. the idle time lost,
  2. the ratio in which the productive times of constituent labour/labor types are mixed and
  3. the actual yield from the labour/labor mix.

  That is the reason, when there are two or more types of labour/labor type being used, the Usage/Gross-Efficiency variance is further broken down into two parts as Efficiency Variance and Idle Time variance and the Efficiency Variance further broken down into Mix Variance and Yield Variance.

• LUV/LGEV = LCV − LRPV
• LUV/LGEV = LEV + LITV
• LUV/LGEV = LMV/GCV + LYV/LSUV + LITV

Verification

Building a table as below would help

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