# Fixed Overhead Absorption Variance

# Illustration - Problem

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.

Calculate overhead variances

Standard | Actual | Absorbed | ||||
---|---|---|---|---|---|---|

Budgeted | for AO | for AI | for AP | |||

A | B | C | ||||

a) Output (units) b) Days c) Time (hrs) d) Overhead Cost 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.

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 |

## Absorbed Cost (Fixed Overhead)

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**= AD × AbR/D Or = SO(AD) × AbR/UO Or = ST(AD) × AbR/UT

## Standard Cost for Actual Output (Fixed Overhead)

Standard Cost for Actual Output ~ **SC(AO)**

= | BC ×
| |||

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 |

## Absorption based on input (time)None | ||

## Absorption based on periods (days)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) d) Overhead Cost 1) Fixed e) Overhead Rate (/Unit) 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) | = |
| ||

= |
| |||

= | 1.025 |

SC(AO) | = | SC ×
| ||

= | 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) d) Overhead Cost 1) Fixed 2) Fixed 3) Total Overhead Ratese) 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 |

Fixed Overhead Absorption Variance

FOHABV | = | AbC − SC(AO) |

= | 82,000 − 82,000 | |

= | 0 |

## Alternatives

Fixed Overhead Absorption Variance

**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)

d) Overhead Cost1) Fixed

2) Fixed

3) Total**Overhead Rates**

e) Per Unit Outputf) Per Unit Input (hr)1) Fixed

2) Fixed

3) Total(d1) ÷ (a)

(d2) ÷ (a)

(d3) ÷ (a)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

82,0002,050

26

22,360

49,200

86,100

1,35,300

82,000

=BR

=BROne 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 Fixed Overhead Absorption Variance

**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)

d) Overhead Cost1) Fixed

2) Fixed

3) Total**Overhead Rates**

e) Per Unit Outputf) Per Unit Input (hr)1) Fixed

2) Fixed

3) Total(d1) ÷ (a)

(d2) ÷ (a)

(d3) ÷ (a)f) Per Unit Period (day)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

82,0002,050

26

22,360

49,200

86,100

1,35,300

82,000

=BR

=BR

=BRSP(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 Fixed Overhead Absorption Variance

**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) d) Overhead Absorption 1) Fixed 2) Fixed 3) Total Overhead Ratese) Rate per Unit 1) Fixed 2) Fixed 3) Total (d1) ÷ (a) (d2) ÷ (a) (d3) ÷ (a) 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 |

| = |
| ||||

= | 1.025 |

SC(AO) | = | BC ×
| ||

= | 80,000 × 1.025 | |||

= | 82,000 |

Fixed Overhead Absorption Variance

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)

d) Overhead Absorption1) Fixed

2) Fixed

3) Total**Overhead Rates**

e) Per Unit Outputf) Per Unit Input (hr)1) Fixed

2) Fixed

3) Total(d1) ÷ (a)

(d2) ÷ (a)

(d3) ÷ (a)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

82,0002,236 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 Fixed Overhead Absorption Variance

**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)

d) Overhead Absorption1) Fixed

2) Fixed

3) Total**Overhead Rates**

e) Rate per Unitf) Per Unit Input (hr)1) Fixed

2) Fixed

3) Total(d1) ÷ (a)

(d2) ÷ (a)

(d3) ÷ (a)g) Per Unit Period (day)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

82,0002,236 2,050

26

22,360

49,200

86,100

1,35,300

89,440

=BR

=BR

=BRSP(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 Fixed Overhead Absorption Variance

**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) d) Overhead Absorption 1) Fixed 2) Fixed 3) Total Overhead Ratese) Per Unit Output 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 40,000 80,000 1,20,000 3,200 | 82,000 | 2,050 26 49,200 86,100 1,35,300 | 83,200 =BR |

| = |
| ||||

= | 1.025 |

SC(AO) | = | BC ×
| ||

= | 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 |

Fixed Overhead Absorption Variance

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)

d) Overhead Absorption1) Fixed

2) Fixed

3) Total**Overhead Rates**

e) Per Unit Outputf) Per Unit Input (hr)1) Fixed

2) Fixed

3) Total(d1) ÷ (a)

(d2) ÷ (a)

(d3) ÷ (a)g) Per Unit Period (day)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

4

3,200

82,000

20,8002,050

26

22,360

49,200

86,100

1,35,300

83,200

=BR

=BR(AP) = (AD) = AD BD = 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 SI(AP) = ST(AD) = BT × AD BD = 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 Fixed Overhead Absorption Variance

**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)

d) Overhead Absorption1) Fixed

2) Fixed

3) Total**Overhead Rates**

e) Per Unit Outputf) Per Unit Input (hr)1) Fixed

2) Fixed

3) Total(d1) ÷ (a)

(d2) ÷ (a)

(d3) ÷ (a)g) Per Unit Period (day)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

82,0002,080

20,8002,050

26

22,360

49,200

86,100

1,35,300

83,200

=BR

=BR

=BRSO(AP) = SO(AD) = BO × AD BD = 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 Fixed Overhead Absorption Variance

**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.### Adverse

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

- 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.