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 Efficiency Variance (VOHExV)
The Variable Overhead Efficiency Variance gives an idea of how much more or less the absorbed variable overhead cost is when compared to the standards.

# • Overheads Absorbed on Unit Rate Basis

## » Calculations based on Output (in Units)

 ⇒ VOHCA AO × BR/U Variable Overhead Cost Absorbed = (Actual Output × Budgeted Rate/unit) =

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, VOEffV = VOHCA − SVOHC
=
(AO × BR/U) − ({AT ×
 BO BT
} × BR/U)

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

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

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

Therefore, VOHEffV = VOHCA − SVOHC
=
({AO ×
 BT BO
} × BR/H) − (AT × BR/H)

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

# • Overheads Absorbed on Time (Hours) Basis

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

 ⇒ VOHCA (AT × BR/H) Variable Overhead Cost Absorbed = (Actual Time × Budgeted Rate/hour) =

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

Therefore, VOEffV = VOHCA − SVOHC
=
(AT × BR/H) − ({AO ×
 BT BO
} × BR/H)

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

## » Calculations based on Output (in Units)

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

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

Therefore, VOHffV = VOHCA − SVOHC
=
({AT ×
 BO BT
} × BR/U) − (AO × BR/U)

♣ 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 choose 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 Efficiency 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 efficiency? This information is provided by the variable overhead efficiency 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)

 ⇒ VOHCA AO × BR/U Variable Overhead Cost Absorbed = (Actual Output × Budgeted Rate/unit) = = 2,050 units × Rs. 20/unit = Rs. 41,000

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

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

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

 ⇒ SVOHC AT × BR/H Standard Variable Overhead Cost = Actual Time × Budgeted Rate/hour = = 22,360 hours × Rs. 2/hour = Rs. 44,720

# • Calculation of Efficiency Variance

⇒ VOHEfV = VOHCA − SVOHC Variable Overhead Efficiency Variance = Variable Overhead Cost Absorbed − Standard Variable Overhead Cost = Rs. 41,000 − Rs. 44,720 = − Rs. 3,720 [Adv]

 Solution [Overheads Absorbed on Time basis]

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

 ⇒ VOHCA (AT × BR/H) Variable Overhead Cost Absorbed = (Actual Time × Budgeted Rate/hour) = = 22,360 hours × Rs. 2/hour = Rs. 44,720

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)

Variable Overhead Cost Absorbed = (Standard Output for Actual Time × Budgeted Rate/Unit)
⇒ VOHCA =
{AT ×
 BO BT
} × BR/U
=
{22,360 hours ×
 2,000 units 20,000 hours
} × Rs. 20/unit
= Rs. 2,236 × 20
= Rs. 44,720

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

# • Calculation of Efficiency Variance

⇒ VOHEfV = VOHCA − SVOHC Variable Overhead Efficiency Variance = Variable Overhead Cost Absorbed − Standard Variable Overhead Cost = Rs. 44,720 − Rs. 41,000 = + Rs. 3,720 [Fav]

 Which method to choose?

 Formulae using Inter-relationships among Variances
1. VOHCV = VOHExpV + VOHEffV   → (1)

From (1)
 VOHEffV = VOHCV − VOHExpV

## • Verification

The interrelationships between variances would also be useful in verifying whether our calculations are correct or not. After calculating the two variable overhead variances we can verify whether VOHExpV and VOHEffV add up to VOHCV or not. If VOHExpV + VOHEffV = VOHCV we can assume our calculations to be correct.

## » Overheads Absorbed on Unit Basis

 VOHExpV + VOHEffV = (− Rs. 4,480) + (− Rs. 3,720) = − Rs. 8,200 = VOHCV   → TRUE

## » Overheads Absorbed on Time Basis

 VOHExpV + VOHEfV = (− Rs. 8,200) + (+ Rs. 3,720) = − Rs. 4,480 = VOHCV   → TRUE
 Author Credit : The Edifier ... Continued Page O:11