The Formulae » Fixed Overhead Cost Variance (FOHCV)



If you have gone through the explanation and formulae for calculating total/variable overhead cost variances, it would be very easy for you to learn this.
Just replace the term Total/Variable with Fixed both in explanations as well as in formulae. For rates, use the fixed overhead rates instead of total/variable overhead rates.

The Fixed Overhead Cost Variance is nothing but Under/Over Absorbed Overhead
⇒ Fixed Overhead Cost Variance = Fixed Overhead Cost Absorbed − Fixed Overhead Cost Incurred
⇒ FOHCV = FOCA  FOCI
Fixed Overhead Cost Incurred

= 
(Actual Output × Actual Rate/unit) 
⇒ FOHCI

= 
(AO × AR/U) 
(Or) 
= 
(Actual Time × Actual Rate/hour) 
(Or) 
= 
(AT × AR/H)

• Note
 Time is measured in hours in most cases. It may be in other units also.
 Actual Rate/unit ⇒ Actual Fixed Overhead Absorption Rate per unit
 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, 
FOCV

= 
FOHCA − FOHCI 


= 
(AO × BR/U) − (AO × AR/U) 
♣ Budgeted Rate/unit ⇒ Budgeted Fixed Overhead Absorption Rate per unit
» 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, 
FOCV

= 
FOHCA − FOHCI 


= 
({AO × 

} × BR/H) − (AT × AR/H) 

♣ Budgeted Rate/hour ⇒ Budgeted Fixed Overhead Absorption Rate per hour
• Overheads Absorbed on Time (Hours) Basis
» Calculations based on Input (Time in Hours)
Fixed Overhead Cost Absorbed

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

= 
(AT × BR/H) 
Therefore, 
FOCV

= 
FOHCA − FOHCI 


= 
(AT × BR/H) − (AT × AR/H) 
♣ Budgeted Rate/hour ⇒ Budgeted Fixed Overhead Absorption Rate per hour
» 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, 
FOCV

= 
FOHCA − FOHCI 


= 
({AT × 

} × BR/U) − (AO × AR/U) 

♣ Budgeted Rate/unit ⇒ Budgeted Fixed 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.


Fixed Overhead Cost 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 fixed overheads?
This information is provided by Fixed Overhead Cost 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 Output (in Units)
Fixed Overhead Cost Absorbed

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

= 
AO × BR/U 

= 
2,050 units × Rs. 40/unit 

= 
Rs. 82,000 
» Calculations Based on Time
Fixed Overhead Cost Absorbed

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

= 


= 
{2,050 units × 

} × Rs. 4/hr 


= 
2,050 units × 10 hrs/unit × Rs. 4/hr 

= 
Rs. 82,000 
• Calculation of Cost Variance
FOHCV 
= 
Absorbed Overhead − Incurred Overhead 

= 
Rs. 82,000 − Rs. 86,100 

= 
− Rs. 4,100 [Adv] 
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)
Fixed Overhead Cost Absorbed

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

= 
(AT × BR/H) 

= 
22,360 hrs × Rs. 4/hr 

= 
Rs. 89,440 
» Calculations Based on Units
Fixed Overhead Cost Absorbed

= 
(Standard Output for Actual Time × Budgeted Rate/Unit) 
⇒ FOHCA

= 


= 
{22,360 hrs × 

} × Rs. 40/unit 


= 
22,360 hrs × 0.1 units/hr × Rs. 40/unit 

= 
Rs. 89,440 
• Calculation of Cost Variance
FOHCV 
= 
Absorbed Overhead − Incurred Overhead 

= 
Rs. 89,440 − Rs. 86,100 

= 
+ Rs. 3,340 [Fav] 
The method of absorption adopted and the method of calculation adopted would influence the calculation of the overhead absorbed only.

With regard to the basis adopted for absorption of overhead we do not have a choice. It is something decided upon by the organisation.
Where the absorption has been made on unit basis, we can arrive at the absorbed overhead using the data relating to time (if it is available). Similarly, where absorption has been made on time basis, we can arrive at the absorbed overhead using the data relating to output (if it is available).
Where data relating to both time and output are available, the first thing that we need to decide upon is the basis for absorption adopted. Where nothing is mentioned, we generally assume that unit basis has been adopted for absorption of overhead. In the absence of data relating to output we may assume that the absorption has been made on time basis also.
Thus availability of data is one another factor that would decide which formula we have to use. However, even in such a case, we need to decide upon the basis for absorption that has been adopted and then use a relevant formula based on the data available.
Be aware that you should not simply replace AT with AO and BR/H with BR/U, as
Absorbed Overhead is equal to
 AT × BR/hr (Or = SO for AT × BR/hr) ← Absorption based on Time
 AO × BR/U (Or = BT for AO × BR/U) ← Absorption based on Units

Formulae using Interrelationships among Variances



 TOHCV = VOHCV + FOHCV → (1)
From (1)
 FOHCV = FOHVolV + FOHExpV → (2)
From (2)
FOHCV = FOHVolV + FOHExpV

 FOHVolV = FOHCalV + FOHCapV + FOHEffV → (3)
From (2) and (3)
FOHCV = FOHCalV + FOHCapV + FOHEffV + FOHExpV

• Verification
The interrelationships between variances would also be useful in verifying whether our calculations are correct or not. After calculating the three variances we can verify whether FOHCV and VOHCV add up to TOHCV or not. If FOHCV + VOHCV = TOHCV we can assume our calculations to be correct.
We used the same set of data in all the explanations. Using the figures obtained for verification.
» Overheads Absorbed based on Output (in units)
TOHCV − VOHCV 
= 
(− Rs. 12,300) − (− Rs. 8,200) 

= 
− Rs. 12,300 + Rs. 8,200 

= 
− Rs. 4,100 

= 
FOHCV 
→ We can assume our calculations to be correct. 
» Overheads Absorbed based on Input (Time in hours)
TOHCV − VOHCV 
= 
(− Rs. 1,140) − (− Rs. 4,480) 

= 
− Rs. 1,140 + Rs. 4,480 

= 
+ Rs. 3,340 

= 
FOHCV 
→ We can assume our calculations to be correct. 


