# Illustration - Problem

A factory was budgeted to produce 2,000 units of output @ one unit per 10 hours productive time working for 25 days. 40,000 for variable overhead cost and 80,000 for 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 49,200 towards variable overheads and 86,100 towards fixed overheads.

Working Table
Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
a) Output (units)
b) Days
c) Time (hrs)
1) Variable
2) Fixed
3) Total
2,000
25

40,000
80,000
1,20,000
2,050
26

49,200
86,100
1,35,300

The working table is populated with the information that can be obtained as it is from the problem data. The rest of the information that is present in a full fledged working table that we make use of in problem solving is filled below.

# Formulae - Fixed Overhead Capacity Variance ~ FOHCAPV

Is there a variation in the actual input and the standard input for the actual periods?

Fixed Overhead Capacity Variance is the difference between the standard fixed overhead cost for actual input and the standard fixed overhead cost for actual periods.

⇒ Fixed Overhead Capacity Variance (FOHCAPV)

 = SC(AI) − SC(AP) Standard Cost for Actual Input − Standard Cost for Actual Periods

## Standard Cost for Actual Input (Fixed Overhead)

Standard Cost for Actual Input ~ SC(AI)

= BC ×
 AI BI
Or = AI × BR/UI
Or = SO(AI) × BR/UO
Or = SP(AI) × BR/UP

## Standard Cost for Actual Periods (Fixed Overhead)

Standard Cost for Actual Periods ~ SC(AI)

= BC ×
 AP BP
Or = AP × BR/UP
Or = SO(AP) × BR/UO
Or = SI(AP) × BR/UI

## Formula in some useful forms

Theoretically any of the forms of the menuend and the subtraend of the formula can be combined to derive various forms of the formula.

As everything leads to finding the value represented, it would be convenient to think in terms of finding the values required and finding the variance using the basic value form of the formula.

However some of the forms are peculiar and they provide a scope to find the variance using a different interpretation of the basic formula. Moreover they would also be useful in interpreting the variance.

FOHCALV = SC(AI) − SC(AP)

Standard Cost for Actual Input − Standard Cost for Actual Periods

Or = BC × (
 AI BI
 AP BP
)

Budgeted Cost × Difference between ratio of actual input to budgeted input and actual periods to budgeted periods

Or = [AI − SI(AP)] × BR/UI

Difference between Actual Input and Standard Input for Actual Periods × Budgeted Rate per unit input

Or = [SO(AI) − SO(AP)] × BR/UO

Difference between Standard Output for Actual Input and Standard Output for Actual Periods × Budgeted Rate per unit output

Or = [SP(AI) − AP] × BR/UP

Difference between Standard Periods for Actual Input and Actual Periods × Budgeted Rate per unit period

## Note

• BC, BR/UO, BR/UI, BR/UP in the above calculations pertains to fixed overheads.
• Theoretically there are many possibilities. Only those that provide peculiar routes to solve problems are given as an academic exercise.
• Finding the costs by building up the working table and using the formula involving costs is the simplest way to find the FOHCAPV.

## Taking time for input and days for periods

Or = BC × (
 AT BT
)
Or = [AT − ST(AD)] × BR/UT
Or = [SO(AT) − SO(AD)] × BR/UO
Or = [SD(AT) − AD] × BR/D

# Solution - (in all cases)

Since the formula for this variance does not involve absorbed overhead, the basis of absorption of overhead is not a factor to be considered in finding this variance.

Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.1181.04
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Variable
2) Fixed
3) Total
2,000
25
20,000

40,000
80,000
1,20,000

89,440

83,200

2,050
26
22,360

49,200
86,100
1,35,300
Data derived through calculations

One unit per 10 hours productive time

⇒ Budgeted Time per unit = 10 hours

Total Budgeted Time

 = Budgeted Output × Budgeted Time/unit = 2,000 units × 10 hrs/unit = 20,000 hrs

Total Actual Time

 = Number of Days × Actual Time/day = 26 days × 860 hrs/day = 22,360 labor/labour hrs
 AI BI
=
 AT BT
=
 22,360 hrs 20,000 hrs
= 1.118
SC(AI) = SC(AT)
= BC ×
 AT BT
= 80,000 × 1.118
= 89,440
 AP BP
=
=
 26 25
= 1.04
= BC ×
= 80,000 × 1.04
= 83,200

 FOHCAPV = SC(AI) − SC(AP) = SC(AT) − SC(AD) = 89,440 − 83,200 = + 6,240 [Fav]

## Alternatives

FOHCAPV = BC × ( AI BI
 AP BP
)
= BC × ( AT BT
−  AP BP
)
= 80,000 × (1.118 − 1.04)
= 80,000 × (0.078)
= + 6,240 [Fav]
• ## Formula in terms of Input (Time)

Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.1181.04
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Variable
2) Fixed
3) Total
1) Variable
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
1) Variable
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
2,000
25
20,000

40,000
80,000
1,20,000

4

89,440

20,800

83,200

2,050
26
22,360

49,200
86,100
1,35,300
Data derived through calculations
= 20,000 hrs × 1.04
= 20,800 hrs

 FOHCAPV = [AI − SI(AP)] × BR/UI = [AT − ST(AD)] × BR/UT = [22,360 hrs − 20,800 hrs] × 4/hr = 1,560 hrs × 4/hr = + 6,240 [Fav]
• ## Formula in terms of Output units

Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.1181.04
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Variable
2) Fixed
3) Total
1) Variable
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
1) Variable
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
2,000
25
20,000

40,000
80,000
1,20,000

40

4
2,236

89,440

2,080

20,800

83,200

2,050
26
22,360

49,200
86,100
1,35,300
Data derived through calculations
SO(AI) = SO(AT)
= BO ×  AT BT
= 2,000 units × 1.118
= 2,236 units
= 2,000 units × 1.04
= 2,080 units

 FOHCAPV = [SO(AI) − SO(AP)] × BR/UO = [SO(AT) − SO(AD)] × BR/UO = [2,236 units − 2,080 units] × 40/unit = 156 units × 40/unit = + 6,240 [Fav]
• ## Formula in terms of Periods

Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.1181.04
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Variable
2) Fixed
3) Total
1) Variable
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
1) Variable
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
2) Fixed
(e2) ÷ (b)
2,000
25
20,000

40,000
80,000
1,20,000

40

4

3,200
2,236
27.95

89,440

2,080

20,800

83,200

2,050
26
22,360

49,200
86,100
1,35,300
Data derived through calculations
SP(AI) = SD(AT)
= BD ×  AT BT
= 25 days × 1.118
= 27.95 days

 FOHCAPV = [SP(AI) − AP] × BR/UP = [SD(AT) − AD] × BR/D = [27.95 days − 26 days] × 3,200/day = 1.95 days × 3,200/day = + 6,240 [Fav]
Theoretically all the forms of the formula can be used for calculations by substituting the values for activity and rates in the formula itself. Using any of them amounts to deriving the values in the formula instead of in the working table.

Building the working table with all the values needed and then using the formula based on values would make the task of finding variances easier.

# Fixed Overhead Capacity Variance - Miscellaneous Aspects

• ## Reasons for variance

The setup is budgeted to work with a certain amount of input during a period. A variation in the actual average input per period from the budgeted input per period would result in a capacity variance.

There would be no capacity variance if average input per period is equal to the budgeted input per period even when the actual number of periods vary from the budgeted periods.

Say the facility is set to work for 1,000 man hours a day for 25 days. There would be capacity variance if the average man hours worked per day is different from 1,000. There would be no capacity variance if the average man hours worked per day is the same as the budgeted man hours per day even if the actual number of days worked is more or less than the budgeted days.

• ## Nature of Variance

Based on the relations derived from the formulae for calculating FOHCAPV, we can identify the nature of Variance

• SC(AI) ___ SC(AP)
•  AI BI
___  AP BP
• AI ___ SI(AP)
• SO(AI) ___ SO(AP)
• SP(AI) ___ AP

The variance would be

• zero when =
• Positive when >
• Negative when <
• ## Interpretation of the Variance

The following interpretations may be made

### No Variance

The actual capacity (in input terms) per unit period is the same as the budgeted capacity for unit period.

### Favourable/Favorable

The actual capacity (in input terms) per unit period is greater than the budgeted capacity for unit period.

A positive variance indicates that there was a benefit on account of having worked to a greater capacity than the one thought of in the budget.

The actual capacity (in input terms) per unit period is lesser than the budgeted capacity for unit period.

The loss is on account of the fact that it was not possible to derive the output with the capacity foregone as the cost would have to be incurred since it is a fixed cost. Cost equal to the cost that might have been incurred for the capacity foregone had the cost not been a fixed cost would be the value of the loss.

• ## Who is answerable for the Variance?

Fixed Overhead Capacity Variance represents the gain or loss on account of the operations being carried on at a lesser/greater capacity than as planned. Those who are authorising capacity utilisation (say working time) would have to answer for the variance.
• ## Where Data relating to Input is not available

In problem solving, where the data relating to input is not available, we assume that there is no capacity variance.

In other words we assume that AI = SI(AP).

This amounts to assuming that the actual inputs have changed in the same proportion as the actual periods compared to the budget, in which case,  AI BI
=  AP BP
• ## Where Data relating to Periods 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.

# Formulae using Inter-relationships among Variances

1. FOHCAPV = FOHVOLV − FOHABSV − FOHEFFV − FOHCALV
2. FOHCAPV = FOHCV − FOHEXPV − FOHABSV − FOHEFFV − FOHCALV

## Verification

The interrelationships between variances would also be useful in verifying whether our calculations are correct or not.

Since the calculation of fixed overhead capacity variance is not influenced by the method of absorption used, the value of the variance would be the same in all cases.

Basis of Absorption
Output Input
(Time)
Periods
(Days)
VOHABSV
+ VOHEFFV
+ VOHEXPV
0
− 3,720
− 4,480
+ 3,720
− 3,720
− 4,480
+ 600
− 3,720
− 4,480
a) VOHCV − 8,200 − 4,480 − 7,600
FOHCALV
+ FOHCAPV
+ FOHEFV

FOHVOLV
FOHEXPV
+ 2,000
− 6,100
+ 9,440
− 6,100
+ 3,200
− 6,100
b) FOHCV − 4,100 + 3,340 − 2,900
TOHCV (a) + (b) − 12,300 − 1,140 − 10,500

To enable understanding we have worked out the illustration under the three possible scenarios of overhead being absorbed on output, input and period basis.

Please be aware that only one of these methods would be in use.