Fixed Overhead Capacity Variance

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Fixed Overhead » Volume Variance = Calendar + Capacity + Efficiency : Variance  
 
The Fixed Overhead Volume variance which is the difference between the absorbed fixed overhead and budgeted fixed overhead is sub divided into three as fixed overhead Calendar variance, Fixed Overhead Capacity Variance and Fixed Overhead Efficiency Variance.

• Mathematical Derivation of the Constituents

Knowing how the volume variance is segregated into calendar, capacity and efficiency may aid your understand and recollection of the formulae.

Where

  1. FOHCA = Fixed Overhead Cost Absorbed
  2. BFOHC = Budgeted Fixed Overhead Cost
  3. FOHVolV = Fixed Overhead Volume Variance
  4. FOHCalV = Fixed Overhead Calendar Variance
  5. FOHCapV = Fixed Overhead Capacity Variance
  6. FOHEffV = Fixed Overhead Efficiency Variance
  7. SFOHC(T/O) = Standard Fixed Overhead Cost for Actual Activity (Time/Output)
  8. SFOHC(D) = Standard Fixed Overhead Cost for Actual Days
Fixed Overhead Volume Variance = Fixed Overhead Absorbed − Budgeted Fixed Overhead
⇒ FOHVolV = FOHCA − BFOHC
= FOHCA − BFOHC + SFOHC(T) − SFOHC(T) + SFOHC(D) − SFOHC(D)
    [Adding and deducting SFOHC(T/O) and SFOHC(D)]
= {FOHCA − SFOHC(T/O)} + {SFOHC(D) − BFOHC} + {SFOHC(T/O) − SFOHC(D)}
= FOHEffV + FOHCalV + FOHCapV
= Efficiency Variance + Calendar Variance + Capacity Variance

• Efficiency Variance

Thus,
Fixed Overhead Efficiency Variance = Fixed Overhead Cost Absorbed
    − Standard Fixed Overhead for Actual Activity (Time/Output)
⇒ FOHEffV = FOHCA − SFOHC(T/O)

• Calendar Variance

Thus,
Fixed Overhead Calendar Variance = Standard Fixed Overhead Cost for Actual Days − Budgeted Fixed Overhead Cost
⇒ FOHCalV = SFOHC(D) − BFOHC

• Capacity Variance

Thus,
Fixed Overhead Capacity Variance = Standard Fixed Overhead Cost for Actual (Time/Output)
    − Standard Fixed Overhead Cost for Actual Days
⇒ FOHCapV = SFOHC(T/O) − SFOHC(D)

Note

  1. Standard Fixed Overhead for Actual Days = Budgeted Fixed Overhead revised for the actual days worked.
  2. Standard Fixed Overhead for Actual Activity (Time/Output)
          = Budgeted Fixed Overhead revised for the actual time worked (Or) actual output.

The Formulae » Fixed Overhead Capacity Variance (FOHCapV)  
 
The Fixed Overhead Capacity Variance gives an idea of how much more or less the standard fixed overhead cost for actual time is when compared to the standard fixed overhead cost for actual days.

⇒ Fixed Overhead Capacity Variance
    = Standard Fixed Overhead Cost for Actual Activity (Time/Output)
        − Standard Fixed Overhead Cost for Actual Days
⇒ FOHCapV = SFOHC(T/O) − SFOHC(D)

Standard Fixed Overhead Cost for Actual Days = Budgeted Fixed Overhead Cost revised for Actual Days
=
Actual Days
Budgeted Days
× Budgeted Fixed Overhead Cost
SFOHC(D) =
AD
BD
× BFOHC

• Overheads Absorbed on Unit Rate Basis

» Calculations based on Units/Time

Standard Fixed Overhead Cost for Actual Activity (Time) = Budgeted Fixed Overhead Cost revised for Actual Time
=
Actual Time
Budgeted Time
× Budgeted Fixed Overhead Cost
SFOHC(T) =
AT
BT
× BFOHC

FOHCapV = SFOHC(T) − SFOHC(D)
=
(
AT
BT
× BFOH) − (
AD
BD
× BFOH)
=
(
AT
BT
AD
BD
) × BFOH

Therefore, FOHCapV =
BFOH × (
AT
BT
AD
BD
)

• Overheads Absorbed on Time Basis

» Calculations based on Units/Time

Standard Fixed Overhead Cost for Actual Activity (Output) = Budgeted Fixed Overhead Cost revised for Actual Output
=
Actual Output
Budgeted Output
× Budgeted Fixed Overhead Cost
SFOHC(O) =
AO
BO
× BFOHC

FOHCapV = SFOHC(O) − SFOHC(D)
=
(
AO
BO
× BFOH) − (
AD
BD
× BFOH)
=
(
AO
BO
AD
BD
) × BFOH

Therefore, FOHCapV =
BFOH × (
AO
BO
AD
BD
)

Capacity Variance » Formula Interpretation  
 

• Where Data relating to Time/Output is not available

Where the data relating to time is not available in the problem, then we assume that there is no capacity variance, i.e. we worked at a capacity that is equal to the planned capacity. In such a case the capacity variance should be zero. This would be so, if we consider the ratio AT/BT to be equal to AD/BD.

• Where Data relating to Days is not available

Where the data relating to days is not available in the problem, then we assume that there is no calendar variance, i.e. we worked for that many days as planned. In such a case the calendar variance should be zero. This would be so, if we consider AD = BD i.e the ratio AD/BD to be equal to 1.

• Where Data relating to both Time/Output as well as Days is not available

Where the data relating to both days and time is not available in the problem, then we assume that there is no capacity as well as calendar variance, i.e. we worked for that many days as planned and at that capacity as planned. In such a case the capacity as well as calendar variances should be zero. This would be so, if we consider AD = BD i.e the ratio AD/BD to be equal to 1 and the ratio AT/BT to be equal to AD/BD i.e. 1.

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 capacity of operations?

This information is provided by the fixed overhead capacity 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
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.

Solution » Working Notes  
 

• 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]  
 

» In all Cases (Calculations Based on Units/Time)

Standard Fixed Overhead Cost for Actual Days =
Actual Days
Budgeted Days
× Budgeted Fixed Overhead Cost
⇒ SFOHC(D) =
AD
BD
× BFOHC
=
26 days
25 days
× Rs. 80,000
= Rs. 1. 04 × 80,000
= Rs. 83,200

Standard Fixed Overhead Cost for Actual Activity (Time) =
Actual Time
Budgeted Time
× Budgeted Fixed Overhead Cost
SFOHC(T) =
AT
BT
× BFOHC
=
22,360 hours
20,000 hours
× Rs. 80,000
= Rs. 1.118 × 80,000
= Rs. 89,440

• Calculation of Variance

FOHCapV = SFOHC(T) − SFOHC(D)
= Rs. 89,440 − Rs. 83,200
= + Rs. 6,240 [Fav]

• Calculation of Variance [Simpler Alternative]

FOHCapV =
BFOH (
AT
BT
AD
BD
)
=
Rs. 80,000 (
22,360 hrs
20,000 hrs
26
25
)
= Rs. 80,000 (1.118 − 1.04)
= + Rs. 80,000 (+ 0.078)
= + Rs. 6,240 [Fav]

Solution [Overheads Absorbed on Time basis]  
 

» In all Cases (Calculations Based on Units/Time)

Standard Fixed Overhead Cost for Actual Days =
Actual Days
Budgeted Days
× Budgeted Fixed Overhead Cost
⇒ SFOHC(D) =
AD
BD
× BFOHC
=
26 days
25 days
× Rs. 80,000
= Rs. 1. 04 × 80,000
= Rs. 83,200

Standard Fixed Overhead Cost for Actual Activity (Output) =
Actual Output
Budgeted Output
× Budgeted Fixed Overhead Cost
SFOHC(O) =
AO
BO
× BFOHC
=
2,050 units
2,000 units
× Rs. 80,000
= Rs. 1.025 × 80,000
= Rs. 82,000

• Calculation of Variance

FOHCapV = SFOHC(O) − SFOHC(D)
= Rs. 82,000 − Rs. 83,200
= − Rs. 1,200 [Adv]

• Calculation of Variance [Simpler Alternative]

FOHCapV =
BFOH (
AO
BO
AD
BD
)
=
(
2,050 units
2,000 units
26
25
) × Rs. 80,000
= (1.025 − 1.04) × Rs. 80,000
= (− 0.015) × Rs. 80,000
= − Rs. 1,200 [Adv]

Formulae using Inter-relationships among Variances  
 
  1. FOHVolV = FOHEffV + FOHCalV + FOHCapV   → (1)

    From (1)
    FOHCapV = FOHVolV − FOHEffV − FOHCalV

  2. FOHCV = FOHVolV + FOHExpV   → (2)

    From (1) and (2)
    FOHCapV = FOHCV − FOHExpV − FOHEffV − FOHCalV

• Verification

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