# Illustration - Problem

7,500 units of a product are planned to be produced using 200 hrs of Skilled Labour/Labor @ 20 per hr, 400 hrs of Semi-Skilled Labour/Labor @ 15/hr and 150 hrs of Unskilled Labour/Labor @ 10 per hr at a total cost of 11,500. 7,200 units of the product were manufactured using 240 hrs of skilled labour/labor @ 22 per hr, 500 hrs of Semi-skilled labour/labor @ 14/hr and 220 hrs of Unskilled labour/labor @ 12 per hr. 20 hrs of Skilled Labour/Labor time, 36 hrs of Semi-Skilled Labour/Labor time and 34 hrs of Unskilled Labour/Labor time were lost due to break down which is abnormal.

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

What is the variation in total cost on account of labour/labor being paid at a rate other than the standard?

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) − AC Standard 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 type
 LRPVLab = SC(AT)Lab − ACLab Or = ATLab × (SRLab − APLab)

## For all Labour/Labor types together

Total Labour/Labor Rate of Pay variance

 TLRPV = ΣLRPVLab Sum of the variances measured for each labour/labor type separately

Labour/Labor Rate of Pay Variance for the mix

 LRPVMix = SC(AT)Mix − ACMix = ATMix × (SRMix − APMix) [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 = LRPVMix, when LRPVMix 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

⇒ V1 = T × R1 → (1)
⇒ V2 = T × R2 → (2)

(1) − (2)

⇒ V1 − V2 = T × R1 − T × R2
⇒ V1 − V2 = T × (R1 − R2)
⇒ 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 formulae for calculating Labour/Labor Rate of Pay Variances involve AT, SR and AR. They do not contain any terms involving standard time (ST). Since recalculation of standard affects standard time (ST) and thereby standard cost (SC) only, we do not need the recalculated standards for finding out labour/labor rate of pay variance.

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) =
 AO SO
=
 7,200 7,500
= 0.96
(AI) =
 AI SI
=
 PTMix STMix
=
 870 750
= 1.16
1. ST(AO) = ST ×
 AO SO
= ST × 0.96

2. SC(AO) = ST(AO) × SR

3. SO(AO) = AO

4. ST(AI) = ST ×
 AI SI
= ST × 1.16

5. SC(AI) = ST(AI) × SR

6. SO(AI) = SO ×
 AI SI
= SO × 1.16

7. AC = AT × AR

8. SC(AT) = AT × SR

# Illustration - Solution

Standards need not be recalculated. But we need SC(AT) and AC for calculating this variance.

LRPV = SC(AT) − AC

Labour/Labor Rate of Pay Variance due to

 Skilled Labour/Labor, LRPVsk = SC(AT)sk − ACsk = 4,800 − 5,280 = − 480 [Adv] Semi Skilled Labour/Labor, LRPVss = SC(AT)ss − ACss = 7,500 − 7,000 = + 500 [Fav] Unskilled Labour/Labor, LRPVus = SC(AT)us − ACus = 2,200 − 2,640 = − 440 [Adv] TLRPV = − 420 [Adv] Labour/Labor Mix, LRPVMix = SC(AT)Mix − ACMix = 14,500 − 14,920 = − 420 [Fav]

# Illustration - Solution (alternative)

If calculating the rate of pay variance is the only requirement, we may avoid calculating the cost/value data in the working table and use the formula involving times and rate. We need only the data relating to AT, SR and AR for this calculation.
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, LRPVsk = ATsk(SRsk − ARsk) = 240 hrs (20/hr − 22/hr) = 240 hrs (− 2/hr) = − 480 [Adv] Semi Skilled Labour/Labor, LRPVss = ATss(SRss − ARss) = 500 hrs (15/hr − 14/hr) = 500 hrs (1/hr) = + 500 [Fav] Unskilled Labour/Labor, LRPVus = ATus(SRus − ARus) = 220 hrs (10/hr − 12/hr) = 220 hrs (− 2/hr) = − 440 [Adv] TLRPV = − 420 [Adv]

Standard Time Mix Ratio

 STMR = STsk : STss : STus = 200 hrs : 400 hrs : 150 hrs = 4 : 8 : 3

Actual Time Mix Ratio

 ATMR = ATsk : ATss : ATus = 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

## LRPVLab

• SC(AT)Lab ___ ACLab
• SRLab ___ ARLab

## LRPVMix

• SC(AT)Mix ___ ACMix
• SRMix ___ ARMix (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.

VarianceMix 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

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 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