Fixed Overheads » Cost Variance = Expenditure Variance + Volume Variance
The Fixed Overhead Cost variance which is the difference between the fixed overhead absorbed and fixed overhead incurred is sub divided into two as fixed overhead expenditure variance and fixed overhead volume 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. FOHCA = Fixed Overhead Cost Absorbed
2. FOHCI = Fixed Overhead Cost Incurred
3. FOHCV = Fixed Overhead Cost Variance
4. FOHExpV = Fixed Overhead Expenditure Variance
5. FOHVolV = Fixed Overhead Volume Variance
6. BFOHC = Budgeted Fixed Overhead Cost

FOHCV FOHCA − FOHCI FOHVolV + FOHExpV Fixed Overhead Cost Variance = Fixed Overhead Absorbed − Fixed Overhead Incurred = = FOHCA − FOHCI + BFOHC − BFOHC     [Adding and deducting BFOHC] = (FOHCA − BFOHC) + (BFOHC − FOHCI) =

# • Volume Variance

Thus,

Volume variance is the difference between the fixed overhead expenditure that should have been incurred (given by the budgeted fixed overheads) and the fixed overheads absorbed.

# • Expenditure Variance

Thus,

Expenditure variance is the difference between the fixed overhead expenditure that should have been incurred (given by the budgeted fixed overheads) and the actual fixed overhead expenditure incurred.

 The Formulae » Fixed Overhead Volume Variance (FOHVolV)

The Fixed Overhead Volume Variance gives an idea of how much more or less the actual fixed overhead cost absorbed is when compared to the budgeted fixed overheads.

# ⇒ Fixed Overhead Volume Variance = Fixed Overhead Cost Absorbed − Budgeted Fixed Overhead Cost ⇒ FOHVolV = FOHCA − BFOHC

BFOHC = BO × BR/U = • Budgeted Fixed Overhead Cost = Budgeted Output × Budgeted Rate per unit (Or) = Budgeted Time × Budgeted Rate per hour (Or)

## » Note

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

# • Overheads Absorbed on Unit Rate Basis

## » Calculations based on Output (in Units)

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

 FOHVolV (AO × BR/U) − (BO × BR/U) Therefore, = FOHCA − BFOHC =

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

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

Therefore, FOHVolV = FOHCA − BFOHC
=
({AO ×
 BT BO
} × BR/H) − (BT × BR/H)

# • Overheads Absorbed on Time (Hour) Basis

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

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

 FOHVolV (AT × BR/H) − (BT × BR/H) Therefore, = FOHCA − BFOHC =

## » Calculations based on Output (in Units)

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

Therefore, FOHVolV = FOHCA − BFOHC
=
({AT ×
 BO BT
} × BR/U) − (BO × BR/U)

 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.

 Fixed Overhead Volume Variance » Formula Interpretation
 The variance would be Nil where the absorbed overhead and the incurred overhead 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 production volume achieved? This information is provided by the fixed overhead volume 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 Units

 = ⇒ FOHCA = Fixed Overhead Cost Absorbed Actual Output × Budgeted Rate/Unit = 2,050 units × Rs. 40/unit = Rs. 82,000

 = ⇒ BFOHC = Budgeted Fixed Overhead Cost Budgeted Output × Budgeted Rate/Unit = Rs. 80,000 [Given]   [(Or) 2,000 units × Rs. 40/unit]

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

Fixed Overhead Cost Absorbed = (Standard Time for Actual Output × Budgeted Rate/hour)
⇒ FOHCA =
{AO ×
 BT BO
} × BR/H
=
{2,050 units ×
 20,000 hours 2,000 units
} × Rs. 4/hour
= Rs. 2,050 × 10 × 4
= Rs. 82,000

 = ⇒ BFOHC = Budgeted Fixed Overhead Cost Budgeted Time × Budgeted Rate/Hour = Rs. 80,000 [Given]   [(Or) 20,000 hours × Rs. 4/hour]

# • Calculation of Variance

⇒ FOHVolV = FOHCA − BFOHC Fixed Overhead Volume Variance = Fixed Overhead Cost Absorbed − Budgeted Fixed Overhead Cost = Rs. 82,000 − Rs. 80,000 = + Rs. 2,000 [Fav]

 Solution [Overheads Absorbed on Time basis]

## » Calculations Based on Time

 ⇒ FOHCA (AT × BR/H) Fixed Overhead Cost Absorbed = (Actual Time × Budgeted Rate/hour) = = 22,360 hours × Rs. 4/hour = 89,440

 = ⇒ BFOHC = Budgeted Fixed Overhead Cost Budgeted Time × Budgeted Rate/Hour = Rs. 80,000 [Given]   [(Or) 20,000 hours × Rs. 4/hour]

## » Calculations Based on Units

Fixed Overhead Cost Absorbed = (Standard Output for Actual Time × Budgeted Rate/Unit)
⇒ FOHCA =
{AT ×
 BO BT
} × BR/U
=
{22,360 hours ×
 2,000 units 20,000 hours
} × Rs. 40/unit
= Rs. 2,236 × 40
= Rs. 89,440

 = ⇒ BFOHC = Budgeted Fixed Overhead Cost Budgeted Output × Budgeted Rate/Unit = Rs. 80,000 [Given]   [(Or) 2,000 units × Rs. 40/unit]

# • Calculation of Variance

⇒ FOHVolV = FOHCA − BFOHC Fixed Overhead Volume Variance = Fixed Overhead Cost Absorbed − Budgeted Fixed Overhead Cost = Rs. 89,440 − Rs. 80,000 = + Rs. 9,440 [Fav]

 Formulae using Inter-relationships among Variances
1. FOHCV = FOHExpV + FOHVolV   → (1)

From (1)
 FOHVolV = FOHCV − FOHExpV

## • Verification

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

## » Overheads Absorbed on Unit Basis

 FOHExpV + FOHEVolV = (− Rs. 6,100) + (+ Rs. 2,000) = − Rs. 4,100 = FOHCV   → TRUE

## » Overheads Absorbed on Time Basis

 FOHExV + FOHVolV = (− Rs. 6,100) + (+ Rs. 9,440) = + Rs. 3,340 = FOHCV   → TRUE
 Author Credit : The Edifier ... Continued Page O:13