# 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 Calendar Variance ~ FOHCALV

Is there a variation between the actual periods worked and budgeted periods planned to be worked?

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

⇒ Fixed Overhead Calendar Variance (FOHCALV)

 = SC(AP) − BC Standard Cost for Actual Periods − Budgeted Cost

## 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

In problem solving the budgeted fixed cost is generally provided as a calculated figure.

Where the budgeted cost is not known we may have to calculate the cost. This calculation requires a measure of budgeted activity and the relevant rate.

Budgeted Cost ~ BC(F)

 = BO × BR/UO Or = BI × BR/UI Or = BP × BR/UP

## 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(AP) − BC

Standard Cost for Actual Periods − Budgeted Cost

Or = BC × (
 AP BP
− 1)

Budgeted Cost × Difference between ratio of actual periods to budgeted periods and 1

Or = [AP − BP] × BR/UP

Difference between Actual Periods and Budgeted Periods × Budgeted Rate per unit period

Or = [SO(AP) − BO] × BR/UO

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

Or = [SI(AP) − BI] × BR/UI

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

## 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 FOHCALV.

## Taking time for input and days for periods

Or = BC × (
 AP BP
− 1)
Or = [AD − BD] × BR/D
Or = [SO(AD) − AO] × BR/UO
Or = [ST(AD) − AT] × BR/UT

# 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 1.04
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
(d2) ÷ (b)
2,000
25

40,000
80,000
1,20,000

3,200

83,200

2,050
26

49,200
86,100
1,35,300
Data derived through calculations
 AP BP
=
=
 26 25
= 1.04
= BC ×
= 80,000 × 1.04
= 83,200

 FOHCALV = SC(AP) − BC = SC(AD) − BC = 83,200 − 80,000 = + 3,200 [Fav]

## Alternatives

FOHCALV = BC × ( AP BP
− 1)
= BC × ( AD BD
− 1)
= 80,000 × (1.04 − 1)
= 80,000 × (0.04)
= + 3,200 [Fav]

 FOHCALV = (AP − BP) × BR/UP = (AD − BD) × BR/D = (26 days − 25 days) × 3,200/day = 1 day × 3,200/day = + 3,200 [Fav]
• ## Formula in terms of Input (Time)

Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.04
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
(d2) ÷ (b)
2,000
25
20,000

40,000
80,000
1,20,000

4

3,200

20,800

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
= 20,000 hrs × 1.04
= 20,800 hrs

 FOHCALV = [SI(AP) − AI] × BR/UI = [ST(AD) − AT] × BR/UT = [20,800 hrs − 20,000 hrs] × 4/hr = 800 hrs × 4/hr = + 3,200 [Fav]
• ## Formula in terms of Output units

Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.04
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
(d2) ÷ (b)
2,000
25
20,000

40,000
80,000
1,20,000

40

4

3,200
2,080

20,800

83,200

2,050
26
22,360

49,200
86,100
1,35,300
Data derived through calculations
= 2,000 units × 1.04
= 2,080 units

 FOHCALV = [SO(AP) − AO] × BR/UO = [SO(AD) − AO] × BR/UO = [2,080 units − 2,000 units] × 40/unit = 80 units × 40/unit = + 3,200 [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.

# Calendar Variance » Formula Interpretation

• ## Reasons for variance

The setup is budgeted to work for a certain number of periods. A variation in the actual number of periods from the budgeted number of periods would result in a calendar variance.

There would be no calendar variance if the number of periods actually worked is the same as that in the budget.

Say the facility is set to work for 25 days. There would be calendar variance if the actual days worked is other than 25.

• ## Nature of Variance

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

• SC(AP) ___ BC
•  AP BP
___ 1
• AP ___ BP
• SO(AP) ___ AO
• SI(AP) ___ AI

The variance would be

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

The following interpretations may be made

### No Variance

The actual number of periods worked is equal to the budgeted periods.

### Favourable/Favorable

The actual number of periods worked is greater than the budgeted periods.

The actual number of periods worked is lesser than the budgeted periods.

The loss is on account of the fact that it was not possible to derive the output with the periods 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 periods foregone had the cost not been a fixed cost would be the value of the loss.

• ## Who is answerable for the Variance?

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

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

In other words we assume that AP = BP.

# Formulae using Inter-relationships among Variances

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

## Verification

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

Since the calculation of fixed overhead calendar 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.