Variable Overheads » Cost Variance = Expenditure Variance + Efficiency Variance
The Variable Overhead Cost variance which is the difference between the variable overhead absorbed and variable overhead incurred is sub divided into two as variable overhead expenditure variance and variable overhead efficiency variance.

# • Mathematical Derivation of the Constituents

Knowing how the cost variance is segregated into expenditure and efficiency may aid your understand and recollection of the formulae.

Where

1. VOHCA = Variable Overhead Cost Absorbed
2. VOHCI = Variable Overhead Cost Incurred
3. VOHCV = Variable Overhead Cost Variance
4. VOHExpV = Variable Overhead Expenditure Variance
5. VOHEffV = Variable Overhead Efficiency Variance
6. SVOHC = Standard Variable Overhead Cost

VOHCV VOHCA − VOHCI VOHEffV + VOHExpV Variable Overhead Cost Variance = Variable Overhead Absorbed − Variable Overhead Incurred = = VOHCA − VOHCI + SVOHC − SVOHC     [Adding and deducting SVOHC] = (VOHCA − SVOHC) + (SVOHC − VOHCI) =

# • Efficiency Variance

Thus,

Efficiency variance is the difference between the variable overheads that should have been incurred as per standards and the overheads that have been absorbed into cost.

# • Expenditure Variance

Thus,

Expenditure variance is the difference between the variable overheads that should have been incurred as per standards and the actual expenditure incurred.

 The Formulae » Variable Overhead Expenditure Variance (VOHExV)
The Variable Overhead Expenditure Variance gives an idea of how much more or less the actual variable overhead cost incurred is when compared to the standards.

# ⇒ Variable Overhead Expenditure Variance = Standard Variable Overhead Cost − Variable Overhead Cost Incurred ⇒ VOHExpV = SVOHC - VOHCI

 ⇒ VOHCI (AO × AR/U) (AT × AR/H) Variable Overhead Cost Incurred = (Actual Output × Actual Rate/unit) = (Or) = (Actual Time × Actual Rate/hour) (Or) =

## • Note

1. Time is measured in hours in most cases. It may be in other units also.
2. Actual Rate/unit ⇒ Actual Variable Overhead Absorption Rate per unit
3. Actual Rate/hour ⇒ Actual Variable Overhead Absorption Rate per hour

# • Overheads Absorbed on Unit Rate Basis

## » Calculations based on Output (in Units)

Standard Variable Overhead Cost = (Standard Output for Actual Time × Budgeted Rate/Unit)
⇒ SVOHC = SO for AT × BR/U
(Or) =
{AT ×
 BO BT
} × BR/U

Therefore, VOExpV = SVOHC − VOHCI
=
({AT ×
 BO BT
} × BR/U) − (AO × AR/U)

♣ Budgeted Rate/unit ⇒ Budgeted Variable Overhead Absorption Rate per unit

## » Calculations based on Input (Time in Hours)

 ⇒ SVOHC AT × BR/H Standard Variable Overhead Cost = Actual Time × Budgeted Rate/hour =

 VOHExpV (AT × BR/H) − (AT × AR/H) Therefore, = SVOHC − VOHCI =

♣ Budgeted Rate/hour ⇒ Budgeted Variable Overhead Absorption Rate per hour

# • Overheads Absorbed on Time (Hours) Basis

## » Calculations based on Input (Time in Hours)

Standard Variable Overhead Cost = (Standard Time for Actual Output × Budgeted Rate/hour)
⇒ SVOHC = ST for AO × BR/H
(Or) =
{AO ×
 BT BO
} × BR/H

Therefore, VOExpV = SVOHC − VOHCI
=
({AO ×
 BT BO
} × BR/H) − (AT × AR/H)

♣ Budgeted Rate/hour ⇒ Budgeted Variable Overhead Absorption Rate per hour

## » Calculations based on Output (in Units)

 ⇒ SVOHC AO × BR/U Standard Variable Overhead Cost = Actual Output × Budgeted Rate/unit =

 VOHExpV (AO × BR/U) − (AO × AR/U) Therefore, = SVOHC − VOHCI =

♣ Budgeted Rate/unit ⇒ Budgeted Variable Overhead Absorption Rate per unit

 The choice of the formula that we use is dependent on two factors The actual basis for absorption used and The basis we chooce for calculations. Care should be taken to ensure that we do not simply interchange the actual units and actual time in calculating absorbed overheads.

 Variable Overhead Expenditure Variance » Formula Interpretation
 The variance would be Nil where the Standard overhead cost and the incurred overhead cost are the same. In problem solving it would be convenient interpreting these formulae in terms of value identifiers rather than the factors that are used to derive value. Thus you need to find the absorbed overhead and there are various formulae for finding the absorbed overhead. This is what you need to remember.

 A Problem
 A factory was to budgeted to produce 2,000 units of output @ one unit per 10 hours productive time working for 25 days. Rs. 40,000 of variable overhead cost and Rs. 80,000 of fixed overhead cost were budgeted to be incurred during that period. The factory worked for 26 days putting in 860 hours work every day and achieved an output of 2,050 units. The expenditure incurred as overheads was Rs. 49,200 as variable overheads and Rs. 86,100 as fixed overheads. What is the variation in total overhead cost on account of a variation in the variable overhead expenditure? This information is provided by the variable overhead expenditure variance

 Solution » Working Table
The problem data arranged in a working table:

Particulars Budgeted Actual
a) Output 2,000 2,050
b) Working Days 25 26
c) Total Time Worked (in hrs) 20,000 22,360
Variable
Fixed
Total

40,000
80,000
1,20,000

49,200
86,100
1,35,300
e) Overhead Rates [(d) ÷ (a)] (in Rs./Unit)
Variable   [(40,000 ÷ 2,000)]
Fixed       [(80,000 ÷ 2,000)]
Total       [(1,20,000 ÷ 2,000)]

20
40
60

f) Overhead Rates [(d) ÷ (c)] (in Rs./hr)
Variable   [(40,000 ÷ 20,000)]
Fixed       [(80,000 ÷ 20,000)]
Total       [(1,20,000 ÷ 20,000)]

2
4
6

## • Note

This working table gives all the data that would be needed to solve a problem involving all overhead variances. In Calculating only the total overhead cost variance you may not need all that data.

We give it here so that you get accustomed to preparing the working table by the time you complete going through all the overhead variances.

 Solution » Working Notes

# » Budgeted Time [BT]

 BT = Budgeted Output × Budgeted Time/unit = 2,000 units × 10 labor/labour hrs/unit [@ one unit per 10 hours productive time] = 20,000 labor/labour hrs

# » Actual Time [AT]

 AT = Number of Days × Actual Time/day = 26 days × 860 labour/labor hrs/day = 22,360 labor/labour hrs

 Solution [Overheads Absorbed on Unit basis]

## » Calculations Based on Output (in Units)

Standard Variable Overhead Cost = (Standard Output for Actual Time × Budgeted Rate/Unit)
⇒ SVOHC =
{AT ×
 BO BT
} × BR/U
=
{22,360 hrs ×
 2,000 units 20,000 hrs
} × Rs. 20/unit
= Rs. 22,360 × 0.1 × 20
= Rs. 44,720

## » Calculations Based Input (Time in Hours)

 ⇒ SVOHC AT × BR/H Standard Variable Overhead Cost = (Actaul Time × Budgeted Rate/Hour) = = 22,360 hrs × Rs. 2/hour = Rs. 44,720

# • Calculation of Expenditure Variance

= Rs. 44,720 − Rs. 49,200

The method of absorption adopted and the method of calculation adopted would influence the calculation of the overhead absorbed only.

 Solution [Overheads Absorbed on Time basis]

## » Calculations Based on Input (Time in hours)

Standard Variable Overhead Cost = (Standard Time for Actual Output × Budgeted Rate/Hour)
⇒ SVOHC =
{AO ×
 BT BO
} × BR/H
=
{2,050 units ×
 20,000 hours 2,000 units
} × Rs. 2/hour
= Rs. 2,050 × 10 × 2
= Rs. 41,000

## • Calculations Based on Output (in Units)

 ⇒ SVOHC AO × BR/U Standard Variable Overhead Cost = (Actaul Output × Budgeted Rate/Unit) = = 2,050 units × Rs. 20/unit = Rs. 41,000

# • Calculation of Expenditure Variance

= Rs. 41,000 − Rs. 49,200

The method of absorption adopted and the method of calculation adopted would influence the calculation of the overhead absorbed only.

 Which method to choose?