# 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 fixed 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 fixed 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) Fixed
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 Absorption Variance ~ FOHABV

The value of Fixed Overhead Absorption Variance provides an answer to this question.

Is the cost absorbed lesser than the standard cost for actual output causing an adversity?

The Fixed Overhead Absorption Variance is the difference between the fixed overhead absorbed and the standard fixed overhead cost for actual output.

⇒ Fixed Overhead Absorption Variance (FOHABV)

 = AbC − SC(AO) Absorbed Cost − Standard Cost for actual output

In problem solving absorbed cost may be provided as a calculated figure. In such a case we do not get concerned about the rate of absorption unless specifically needed in some calculation.

Where the absorbed cost is not known we may have to calculate the cost. This calculation is based on the rate of absorption that has been used in the context to absorb total overheads.

• ### Absorption based on output (units)

Absorbed Cost ~ AbC

 = AO × AbR/UO Or = ST(AO) × AbR/UT Or = SD(AO) × AbR/D
• ### Absorption based on inputs (time)

Absorbed Cost ~ AbC

 = AT × AbR/UT Or = SO(AT) × AbR/UO Or = SD(AT) × AbR/D
• ### Absorption based on periods (days)

Absorbed Cost ~ AbC

## Standard Cost for Actual Output (Fixed Overhead)

Standard Cost for Actual Output ~ SC(AO)

= BC ×
 AO BO
Or = AO × BR/UO
Or = ST(AO) × BR/UT
Or = SD(AO) × BR/D

## Formula in useful forms

FOHABV = AbC − SC(AO)

Absorbed Cost − Standard Cost for Actual Output

### Absorption based on output units

Or = AO × (AbR/UO − BR/UO)

Actual Output × Difference between Absorbed and Budgeted Rates per unit

Or = ST(AO) × (AbR/UT − BR/UT)

Standard Time for Actual Output × Difference between Absorption Rate per unit time and Budgeted Rate per unit time

Or = SD(AO) × (AbR/D − BR/D)

Standard Days for Actual Output × Difference between Absorption Rate per day and Budgeted Rate per day

None

None

## Note

• AbR/UO, AbR/UT, AbR/D 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 FOHABV.

# Solution - Working Notes

Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.025
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Fixed
2) Fixed
3) Total
1) Fixed
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (b)
(d2) ÷ (b)
(d3) ÷ (b)
2,000
25
20,000

40,000
80,000
1,20,000

40

4

3,200

25.625
20,500

82,000

2,050
26
22,360

49,200
86,100
1,35,300

24

41,000

=BR

=BR

=BR

(AO) =
 AO BO
=
 2,050 units 2,000 units
= 1.025
SC(AO) = SC ×
 AO BO
= SC × 1.025
 SC(AO)(V) = SC(V) × 1.025 = 40,000 × 1.025 = 41,000 SC(AO)(F) = SC(F) × 1.025 = 80,000 × 1.025 = 82,000 SC(AO)(T) = SC(AO)(V) + SC(AO)(F) = 41,000 × 82,000 = 1,23,000

# Solution - (Assuming absorption is based on Output)

## No Absorption Variance

Where absorption is being done based on output units and absorption rate is the budgeted rate and the Fixed Overhead Cost Variance is assumed to have been sub divided into three components, Capacity Variance, Calendard Variance and Efficiency Variance, Fixed Overhead Absorption Variance does not exist.

## Absorption Variance is Zero

Where absorption is being done based on output units and absorption rate is the budgeted rate and the Fixed Overhead Cost Variance is assumed to have been sub divided into four components, Absorption Variance, Capacity Variance, Calendard Variance and Efficiency Variance, Fixed Overhead Absorption Variance would be zero.
Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.025
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Fixed
2) Fixed
3) Total
e) Per Unit Output
1) Fixed
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
2,000
25

40,000
80,000
1,20,000

40

82,000

2,050
26

49,200
86,100
1,35,300

82,000

=BR

In the absence of information to the contrary we assume

 AbR/UO(F) = BR/UO(F) = 40

Absorbed Fixed Overhead Cost ~ AbC(F)

 = AO × AbR/UO(F) = 2,050 units × 40/unit = 82,000

 FOHABV = AbC − SC(AO) = 82,000 − 82,000 = 0

## Alternatives

 FOHABV = AO × (AbR/UO − BR/UO) = 2,050 units × (40/unit − 40/unit) = 2,050 units × (0) = 0
• ## Calculations based on input

The absorbed overhead may be ascertained using SI(AO) and AbR/UI.
Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.025
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Fixed
2) Fixed
3) Total
e) Per Unit Output
1) Fixed
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
f) Per Unit Input (hr)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
2,000
25
20,000

40,000
80,000
1,20,000

40

4

20,500

82,000

2,050
26
22,360

49,200
86,100
1,35,300

82,000

=BR

=BR

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 hrs
SI(AO) = ST(AO)
= BT ×  AO BO
= 20,000 hrs × 1.025
= 20,500 hrs

In the absence of information to the contrary we assume

 AbR/UT(F) = BR/UT(F) = 4

Absorbed Fixed Overhead Cost ~ AbC(F)

 = SI(AO) × AbR/UI(F) = ST(AO) × AbR/UT(F) = 20,500 hrs × 4/hr = 82,000

 FOHABV = AbC − SC(AO) = 82,000 − 82,000 = 0 Or = SI(AO) × (AbR/UI − BR/UI) = ST(AO) × (AbR/UT − BR/UT) = 22,360 hrs × (4/hr − 4/hr) = 22,360 hrs × (0) = 0
• ## Calculations based on periods

The absorbed overhead may be ascertained using SP(AO) and AbR/UP.
Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.025
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Fixed
2) Fixed
3) Total
e) Per Unit Output
1) Fixed
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
f) Per Unit Input (hr)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
f) Per Unit Period (day)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (b)
(d2) ÷ (b)
(d3) ÷ (b)
2,000
25
20,000

40,000
80,000
1,20,000

40

4

3,200

25.625
20,500

82,000

2,050
26
22,360

49,200
86,100
1,35,300

82,000

=BR

=BR

=BR
SP(AO) = SD(AO)
= BD ×  AO BO
= 25 days × 1.025
= 25.625 days

In the absence of information to the contrary we assume

 AbR/D(F) = BR/D(F) = 3,200

Absorbed Fixed Overhead Cost ~ AbC(F)

 = SP(AO) × AbR/UP(F) = SD(AO) × AbR/D(F) = 25.625 days × 3,200/day = 82,000

 FOHABV = AbC − SC(AO) = 82,000 − 82,000 = 0 Or = SP(AO) × (AbR/UP − BR/UP) = SD(AO) × (AbR/D − BR/D) = 25.625 days × (3,200/day − 3,200/day) = 25.625 days × (0) = 0

# Solution - (Assuming absorption is based on Input)

Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.025
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Fixed
2) Fixed
3) Total
e) Rate per Unit
1) Fixed
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
f) Per Unit Input (hr)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
2,000
25
20,000

40,000
80,000
1,20,000

4

82,000
2,050
26
22,360

49,200
86,100
1,35,300

89,440

=BR

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 hrs

In the absence of information to the contrary we assume

 AbR/UT(F) = BR/UT(F) = 4/hr

Absorbed Fixed Overhead Cost ~ AbC(F)

 = AO × AbR/UT(F) = 22,360 hrs × 2/hr = 89,440
 AO BO
=
 2,050 units 2,000 units
= 1.025
SC(AO) = BC ×
 AO BO
= 80,000 × 1.025
= 82,000

 FOHABV = AbC − SC(AO) = 89,440 − 82,000 = + 7,440 [Fav]

## Alternatives

Where absorption is based on inputs, there are no formulae in alternate forms for finding the fixed overhead absorption variance. The ones shown below are for finding the absorbed cost in an alternative manner.
• ## Calculations based on output

The absorbed overhead may be ascertained using SO(AI) and AbR/UO.
Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.025 1.118
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Fixed
2) Fixed
3) Total
e) Per Unit Output
1) Fixed
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
f) Per Unit Input (hr)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
2,000
25
20,000

40,000
80,000
1,20,000

40

4

82,000
2,236

2,050
26
22,360

49,200
86,100
1,35,300

89,440

=BR

=BR

(AI) = (AT)
=  AT BT
=  22,360 hrs 20,000 hrs
= 1.118
SO(AI) = SO(AT)
= BO ×  AT BT
= 2,000 units × 1.118
= 2,236 units

In the absence of information to the contrary we assume

 AbR/UO(F) = BR/UO(F) = 40

Absorbed Fixed Overhead Cost ~ Abc(F)

 = SO(AI) × AbR/UO(F) = SO(AT) × AbR/UO(F) = 2,236 units × 40/unit = 89,440

 FOHABV = AbC − SC(AO) = 89,440 − 82,000 = + 7,440 [Fav]
• ## Calculations based on periods

The absorbed overhead may be ascertained using SP(AI) and AbR/UP.
Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.025 1.118
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Fixed
2) Fixed
3) Total
e) Rate per Unit
1) Fixed
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
f) Per Unit Input (hr)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
g) Per Unit Period (day)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (b)
(d2) ÷ (b)
(d3) ÷ (b)
2,000
25
20,000

40,000
80,000
1,20,000

40

4

3,200

82,000
2,236

2,050
26
22,360

49,200
86,100
1,35,300

89,440

=BR

=BR

=BR

SP(AI) = SD(AT)
= BD ×  AT BT
= 25 days × 1.118
= 27.95 days

In the absence of information to the contrary we assume

 AbR/D(F) = BR/D(F) = 3,200

Absorbed Fixed Overhead Cost ~ Abc(F)

 = SP(AO) × AbR/UP(F) = SD(AO) × AbR/D(F) = 27.95 days × 3,200/day = 89,440

 FOHABV = AbC − SC(AO) = 89,440 − 82,000 = + 7,440 [Fav]

# Solution - (Assuming absorption is based on Periods)

Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.025
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Fixed
2) Fixed
3) Total
e) Per Unit Output
1) Fixed
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
f) Per Unit Input (hr)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
g) Per Unit Period (day)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (b)
(d2) ÷ (b)
(d3) ÷ (b)
2,000
25

40,000
80,000
1,20,000

3,200

82,000
2,050
26

49,200
86,100
1,35,300

83,200

=BR

 AO BO
=
 2,050 units 2,000 units
= 1.025
SC(AO) = BC ×
 AO BO
= 80,000 × 1.025
= 42,000

In the absence of information to the contrary we assume

 AbR/D(F) = BR/D(F) = 3,200/day

Absorbed Fixed Overhead Cost ~ AbC(F)

 = AD × AbR/D(F) = 26 days × 3,200/day = 83,200

 FOHABV = AbC − SC(AO) = 83,200 − 82,000 = + 1,200 [Fav]

## Alternatives

Where absorption is based on periods, days here, there are no formulae in alternate forms for finding the fixed overhead absorption variance. The ones shown below are for finding the absorbed cost in an alternative manner.
• ## Calculations based on inputs

The absorbed overhead may be ascertained using SI(AP) and AbR/UI.
Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.025 1.04
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Fixed
2) Fixed
3) Total
e) Per Unit Output
1) Fixed
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
f) Per Unit Input (hr)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
g) Per Unit Period (day)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (b)
(d2) ÷ (b)
(d3) ÷ (b)
2,000
25
20,000

40,000
80,000
1,20,000

4

3,200

82,000

20,800
2,050
26
22,360

49,200
86,100
1,35,300

83,200

=BR

=BR

=  26 days 25 days
= 1.04

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 hrs
= 20,000 hrs × 1.04
= 20,800 hrs

In the absence of information to the contrary we assume

 AbR/UT(F) = BR/UT(F) = 4

Absorbed Fixed Overhead Cost ~ Abc(F)

 = SI(AP) × AbR/UI(F) = ST(AD) × AbR/UT(F) = 20,800 hrs × 4/hr = 83,200

 FOHABV = AbC − SC(AO) = 83,200 − 82,000 = + 1,200 [Fav]
• ## Calculations based on output

The absorbed overhead may be ascertained using SO(AP) and AbR/UO.
Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.025 1.04
a) Output (units)
b) Periods (Days)
c) Time (hrs)
1) Fixed
2) Fixed
3) Total
e) Per Unit Output
1) Fixed
2) Fixed
3) Total
(d1) ÷ (a)
(d2) ÷ (a)
(d3) ÷ (a)
f) Per Unit Input (hr)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (c)
(d2) ÷ (c)
(d3) ÷ (c)
g) Per Unit Period (day)
1) Fixed
2) Fixed
3) Total
(d1) ÷ (b)
(d2) ÷ (b)
(d3) ÷ (b)
2,000
25
20,000

40,000
80,000
1,20,000

40

4

3,200

82,000
2,080

20,800
2,050
26
22,360

49,200
86,100
1,35,300

83,200

=BR

=BR

=BR

= 2,000 units × 1.04
= 2,080 units

In the absence of information to the contrary we assume

 AbR/UO(F) = BR/UO(F) = 40

Absorbed Fixed Overhead Cost ~ Abc(F)

 = SO(AD) × AbR/UO(F) = 2,080 units × 40/unit = 83,200

 FOHABV = AbC − SC(AO) = 83,200 − 82,000 = + 1,200 [Fav]

# Fixed Overhead Absorption Variance - Miscellaneous Aspects

• ## Nature of Variance

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

• AbC ___ SC(AO)
• One that is relevant from these depending on the basis for absorption used

• AbR/UO ___ BR/UO
• AbR/UI ___ BR/UI
• AbR/UP ___ BR/UP

The variance would be

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

The following interpretations may be made

### No Variance

Cost equal to the standard fixed overhead cost for the actual output has been absorbed.

### Favourable/Favorable

Cost greater than the standard fixed overhead cost for the actual output has been absorbed.

Cost lesser than the standard fixed overhead cost for the actual output has been absorbed.
• ## Who is answerable for the Variance?

Since the cost being absorbed is different from the standard cost for actual output, the ones who are responsible for fixing the basis and rate of absorption of overhead would be answerable for the variance.

# Formulae using Inter-relationships among Variances

1. FOHABV = FOHCV − FOHEFV − FOHEXV

## Verification

The interrelationships between variances would also be useful in verifying whether our calculations are correct or not.
Basis of Absorption
Output Input
(Time)
Periods
(Days)
VOHABSV
+ VOHEFFV
+ VOHEXPV
0

+ 3,720

+ 600

a) VOHCV − 8,200 − 4,480 − 7,600
FOHCALV
+ FOHCAPV
+ FOHEFV

FOHVOLV
FOHEXPV

b) FOHCV
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.