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
 FOHCA = Fixed Overhead Cost Absorbed
 FOHCI = Fixed Overhead Cost Incurred
 FOHCV = Fixed Overhead Cost Variance
 FOHExpV = Fixed Overhead Expenditure Variance
 FOHVolV = Fixed Overhead Volume Variance
 BFOHC = Budgeted Fixed Overhead Cost
Fixed Overhead Cost Variance 
= 
Fixed Overhead Absorbed − Fixed Overhead Incurred 
FOHCV 
= 
FOHCA − FOHCI 

= 
FOHCA − FOHCI + BFOHC − BFOHC
[Adding and deducting BFOHC]


= 
(FOHCA − BFOHC) + (BFOHC − FOHCI) 

= 
FOHVolV + FOHExpV 
• Volume Variance
Thus,
Fixed Overhead Volume Variance 
= 
Fixed Overhead Cost Absorbed − Budgeted Fixed Overhead Cost 
⇒ FOHVolV 
= 
FOHCA − BFOHC 
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,
Fixed Overhead Expenditure Variance 
= 
Budgeted Fixed Overhead Cost − Fixed Overhead Cost Incurred 
⇒ FOHExpV 
= 
BFOHC − FOHCI 
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
• Budgeted Fixed Overhead Cost 
= 
Budgeted Output × Budgeted Rate per unit 
BFOHC 
= 
BO × BR/U 
(Or) 
= 
Budgeted Time × Budgeted Rate per hour 
(Or) 
= 
BT × BR/H 
» Note

 Time is measured in hours in most cases. It may be in other units also.
 Budgeted Rate/unit ⇒ Budgeted Fixed Overhead Absorption Rate per unit
 Actual Rate/unit ⇒ Actual Fixed Overhead Absorption Rate per unit
 Budgeted Rate/hour ⇒ Budgeted Fixed Overhead Absorption Rate per hour
 Actual Rate/hour ⇒ Actual Fixed Overhead Absorption Rate per hour
• Overheads Absorbed on Unit Rate Basis
» Calculations based on Output (in Units)
Fixed Overhead Cost Absorbed

= 
(Actual Output × Budgeted Rate/unit) 
⇒ FOHCA

= 
AO × BR/U 
Therefore, 
FOHVolV

= 
FOHCA − BFOHC 


= 
(AO × BR/U) − (BO × BR/U) 
» 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)

= 

Therefore, 
FOHVolV

= 
FOHCA − BFOHC 


= 
({AO × 

} × BR/H) − (BT × BR/H) 

• Overheads Absorbed on Time (Hour) Basis
» Calculations based on Input (Time in Hours)
Fixed Overhead Cost Absorbed

= 
(Actual Time × Budgeted Rate/hour) 
⇒ FOHCA

= 
(AT × BR/H) 
Therefore, 
FOHVolV

= 
FOHCA − BFOHC 


= 
(AT × BR/H) − (BT × BR/H) 
» 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)

= 

Therefore, 
FOHVolV

= 
FOHCA − BFOHC 


= 
({AT × 

} × 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 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

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 
d) Overhead Cost (in Rs.)
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.

• Working Time
» 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
Fixed Overhead Cost Absorbed 
= 
Actual Output × Budgeted Rate/Unit 
⇒ FOHCA 
= 
(AO × BR/U) 

= 
2,050 units × Rs. 40/unit 

= 
Rs. 82,000 
Budgeted Fixed Overhead Cost 
= 
Budgeted Output × Budgeted Rate/Unit 
⇒ BFOHC 
= 
(BO × BR/U) 

= 
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

= 


= 
{2,050 units × 

} × Rs. 4/hour 


= 
Rs. 2,050 × 10 × 4 

= 
Rs. 82,000 
Budgeted Fixed Overhead Cost 
= 
Budgeted Time × Budgeted Rate/Hour 
⇒ BFOHC 
= 
(BT × BR/H) 

= 
Rs. 80,000 [Given] [(Or) 20,000 hours × Rs. 4/hour] 
• Calculation of Variance
Fixed Overhead Volume Variance 
= 
Fixed Overhead Cost Absorbed − Budgeted Fixed Overhead Cost 
⇒ FOHVolV 
= 
FOHCA − BFOHC 

= 
Rs. 82,000 − Rs. 80,000 

= 
+ Rs. 2,000 [Fav] 

Solution [Overheads Absorbed on Time basis]



» Calculations Based on Time
Fixed Overhead Cost Absorbed

= 
(Actual Time × Budgeted Rate/hour) 
⇒ FOHCA

= 
(AT × BR/H) 

= 
22,360 hours × Rs. 4/hour 

= 
89,440 
Budgeted Fixed Overhead Cost 
= 
Budgeted Time × Budgeted Rate/Hour 
⇒ BFOHC 
= 
(BT × BR/H) 

= 
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

= 


= 
{22,360 hours × 

} × Rs. 40/unit 


= 
Rs. 2,236 × 40 

= 
Rs. 89,440 
Budgeted Fixed Overhead Cost 
= 
Budgeted Output × Budgeted Rate/Unit 
⇒ BFOHC 
= 
(BO × BR/U) 

= 
Rs. 80,000 [Given] [(Or) 2,000 units × Rs. 40/unit] 
• Calculation of Variance
Fixed Overhead Volume Variance 
= 
Fixed Overhead Cost Absorbed − Budgeted Fixed Overhead Cost 
⇒ FOHVolV 
= 
FOHCA − BFOHC 

= 
Rs. 89,440 − Rs. 80,000 

= 
+ Rs. 9,440 [Fav] 

Formulae using Interrelationships among Variances



 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 


