# Variable 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 variable 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) 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 - Variable Overhead Absorption Variance ~ VOHABSV

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

⇒ Variable Overhead Absorption Variance (**VOHABSV**)

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

## Absorbed Cost (Variable 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

Absorbed Cost ~

**AbC**= AO × AbR/UO Or = SI(AO) × AbR/UI Or = SP(AO) × AbR/UP ### Absorption based on inputs

Absorbed Cost ~

**AbC**= AI × AbR/UI Or = SO(AI) × AbR/UO Or = SP(AI) × AbR/UP ### Absorption based on periods

Absorbed Cost ~

**AbC**= AP × AbR/UP Or = SO(AP) × AbR/UO Or = SI(AP) × AbR/UI

## Standard Cost for Actual Output (Variable Overhead)

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

= | BC ×
| |||

Or | = | AO × BR/UO | ||

Or | = | SI(AO) × BR/UI | ||

Or | = | SP(AO) × BR/UP |

## Formula in useful forms

VOHABSV | = | 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 output |

Or | = | SI(AO) × (AbR/UI − BR/UI) Standard Input for Actual Output × Difference between Absorption Rate per unit input and Budgeted Rate per unit input |

Or | = | SP(AO) × (AbR/UP − BR/UP) Standard Periods for Actual Output × Difference between Absorption Rate per unit period and Budgeted Rate per unit period |

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

## Absorption based on periods (days)None |

## Note

- AbR/UO, AbR/UI, AbR/UP in the above calculations pertains to variable 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 VOHABSV.

## Taking time for input and days for periods

VOHABSV | = | AbC − SC(AO) |

Or | = | AO × [AbR/UO − BR/UO] |

Or | = | ST(AO) × [AbR/UT − BR/UT] |

Or | = | SD(AO) × [AbR/D − BR/D] |

# 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 Variable Overhead Cost Variance is assumed to have been sub divided into two components, Efficiency Variance and Expenditure Variance, Variable 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 Variable Overhead Cost Variance is assumed to have been sub divided into three components, Absorption Variance, Efficiency Variance and Expenditure Variance, Variable 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) Variable 2) Fixed 3) Total Overhead Ratese) Per Unit Output 1) Variable 2) Fixed 3) Total (d1) ÷ (a) (d2) ÷ (a) (d3) ÷ (a) | 2,000 25 40,000 80,000 1,20,000 20 | 41,000 | 2,050 26 49,200 86,100 1,35,300 | 41,000 =BR |

In the absence of information to the contrary we assume

AbR/UO(V) | = | BR/UO(V) |

= | 20 |

Absorbed Variable Overhead Cost ~ AbC(V)

= | AO × AbR/UO(V) |

= | 2,050 units × 20/unit |

= | 41,000 |

Variable Overhead Absorption Variance

VOHABSV | = | AbC − SC(AO) |

= | 41,000 − 41,000 | |

= | 0 |

## Alternatives

Variable Overhead Absorption Variance

**VOHABSV**= **AO × (AbR/UO − BR/UO)**= 2,050 units × (20/unit − 20/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) Variable

2) Fixed

3) Total**Overhead Rates**

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

20

2

20,500

41,0002,050

26

22,360

49,200

86,100

1,35,300

41,000

=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(V) = BR/UT(V) = 2 Absorbed Variable Overhead Cost ~ AbC(V)

= **SI(AO) × AbR/UI(V)**= ST(AO) × AbR/UT(V) = 20,500 hrs × 2/hr = 41,000 Variable Overhead Absorption Variance

**VOHABSV**= **AbC − SC(AO)**= 41,000 − 41,000 = 0 Or = **SI(AO) × (AbR/UI − BR/UI)**= ST(AO) × (AbR/UT − BR/UT) = 22,360 hrs × (2/hr − 2/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) Variable

2) Fixed

3) Total**Overhead Rates**

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

2) Fixed

3) Total(d1) ÷ (a)

(d2) ÷ (a)

(d3) ÷ (a)f) Per Unit Period (day)1) Variable

2) Fixed

3) Total(d1) ÷ (c)

(d2) ÷ (c)

(d3) ÷ (c)1) Variable

2) Fixed

3) Total(d1) ÷ (b)

(d2) ÷ (b)

(d3) ÷ (b)2,000

25

20,000

40,000

80,000

1,20,000

20

2

1,600

25.625

20,500

41,0002,050

26

22,360

49,200

86,100

1,35,300

41,000

=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(V) = BR/D(V) = 1,600 Absorbed Variable Overhead Cost ~ AbC(V)

= **SP(AO) × AbR/UP(V)**= SD(AO) × AbR/D(V) = 25.625 days × 1,600/day = 41,000 Variable Overhead Absorption Variance

**VOHABSV**= **AbC − SC(AO)**= 41,000 − 41,000 = 0 Or = **SP(AO) × (AbR/UP − BR/UP)**= SD(AO) × (AbR/D − BR/D) = 25.625 days × (1,600/day − 1,600/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) Variable 2) Fixed 3) Total Overhead Ratese) Rate per Unit 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 2 | 41,000 | 2,050 26 22,360 49,200 86,100 1,35,300 | 44,720 =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(V) | = | BR/UT(V) |

= | 2/hr |

Absorbed Variable Overhead Cost ~ AbC(V)

= | AO × AbR/UT(V) |

= | 22,360 hrs × 2/hr |

= | 44,720 |

| = |
| ||||

= | 1.025 |

SC(AO) | = | BC ×
| ||

= | 40,000 × 1.025 | |||

= | 41,000 |

Variable Overhead Absorption Variance

VOHABSV | = | AbC − SC(AO) |

= | 44,720 − 41,000 | |

= | + 3,720 [Fav] |

## Alternatives

Where absorption is based on inputs, there are no formulae in alternate forms for finding the variable 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) Variable

2) Fixed

3) Total**Overhead Rates**

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

20

2

41,0002,236 2,050

26

22,360

49,200

86,100

1,35,300

44,720

=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(V) = BR/UO(V) = 20 Absorbed Variable Overhead Cost ~ Abc(V)

= **SO(AI) × AbR/UO(V)**= SO(AT) × AbR/UO(V) = 2,236 units × 20/unit = 44,720 Variable Overhead Absorption Variance

**VOHABSV**= **AbC − SC(AO)**= 44,720 − 41,000 = + 3,720 [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) Variable

2) Fixed

3) Total**Overhead Rates**

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

2) Fixed

3) Total(d1) ÷ (a)

(d2) ÷ (a)

(d3) ÷ (a)g) Per Unit Period (day)1) Variable

2) Fixed

3) Total(d1) ÷ (c)

(d2) ÷ (c)

(d3) ÷ (c)1) Variable

2) Fixed

3) Total(d1) ÷ (b)

(d2) ÷ (b)

(d3) ÷ (b)2,000

25

20,000

40,000

80,000

1,20,000

20

2

1,600

41,0002,236 2,050

26

22,360

49,200

86,100

1,35,300

44,720

=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(V) = BR/D(V) = 1,600 Absorbed Variable Overhead Cost ~ Abc(V)

= **SP(AO) × AbR/UP(V)**= SD(AO) × AbR/D(V) = 27.95 days × 1,600/day = 44,720 Variable Overhead Absorption Variance

**VOHABSV**= **AbC − SC(AO)**= 44,720 − 41,000 = + 3,720 [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) Variable 2) Fixed 3) Total Overhead Ratese) Per Unit Output 1) Variable 2) Fixed 3) Total (d1) ÷ (a) (d2) ÷ (a) (d3) ÷ (a) 1) Variable 2) Fixed 3) Total (d1) ÷ (c) (d2) ÷ (c) (d3) ÷ (c) 1) Variable 2) Fixed 3) Total (d1) ÷ (b) (d2) ÷ (b) (d3) ÷ (b) | 2,000 25 40,000 80,000 1,20,000 1,600 | 41,000 | 2,050 26 49,200 86,100 1,35,300 | 41,600 =BR |

| = |
| ||||

= | 1.025 |

SC(AO) | = | BC ×
| ||

= | 40,000 × 1.025 | |||

= | 41,000 |

In the absence of information to the contrary we assume

AbR/D(V) | = | BR/D(V) |

= | 1,600/day |

Absorbed Variable Overhead Cost ~ AbC(V)

= | AD × AbR/D(V) |

= | 26 days × 1,600/day |

= | 41,600 |

Variable Overhead Absorption Variance

VOHABSV | = | AbC − SC(AO) |

= | 41,600 − 41,000 | |

= | + 600 [Fav] |

## Alternatives

Where absorption is based on periods, days here, there are no formulae in alternate forms for finding the variable 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) Variable

2) Fixed

3) Total**Overhead Rates**

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

2) Fixed

3) Total(d1) ÷ (a)

(d2) ÷ (a)

(d3) ÷ (a)g) Per Unit Period (day)1) Variable

2) Fixed

3) Total(d1) ÷ (c)

(d2) ÷ (c)

(d3) ÷ (c)1) Variable

2) Fixed

3) Total(d1) ÷ (b)

(d2) ÷ (b)

(d3) ÷ (b)2,000

25

20,000

40,000

80,000

1,20,000

2

1,600

41,000

20,8002,050

26

22,360

49,200

86,100

1,35,300

41,600

=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(V) = BR/UT(V) = 2 Absorbed Variable Overhead Cost ~ Abc(V)

= **SI(AP) × AbR/UI(V)**= ST(AD) × AbR/UT(V) = 20,800 hrs × 2/hr = 41,600 Variable Overhead Absorption Variance

**VOHABSV**= **AbC − SC(AO)**= 41,600 − 41,000 = + 600 [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) Variable

2) Fixed

3) Total**Overhead Rates**

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

2) Fixed

3) Total(d1) ÷ (a)

(d2) ÷ (a)

(d3) ÷ (a)g) Per Unit Period (day)1) Variable

2) Fixed

3) Total(d1) ÷ (c)

(d2) ÷ (c)

(d3) ÷ (c)1) Variable

2) Fixed

3) Total(d1) ÷ (b)

(d2) ÷ (b)

(d3) ÷ (b)2,000

25

20,000

40,000

80,000

1,20,000

20

2

1,600

41,0002,080

20,8002,050

26

22,360

49,200

86,100

1,35,300

41,600

=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(V) = BR/UO(V) = 20 Absorbed Variable Overhead Cost ~ Abc(V)

= SO(AD) × AbR/UO(V) = 2,080 units × 20/unit = 41,600 Variable Overhead Absorption Variance

**VOHABSV**= **AbC − SC(AO)**= 41,600 − 41,000 = + 600 [Fav]

# Variable Overhead Absorption Variance - Miscellaneous Aspects

## Nature of Variance

Based on the relations derived from the formulae for calculating VOHCV, 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 variable overhead cost for the actual output has been absorbed.### Favourable/Favorable

Cost greater than the standard variable overhead cost for the actual output has been absorbed.### Adverse

Cost lesser than the standard variable 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

- VOHABSV = VOHCV − VOHEFFV − VOHEXPV

## 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.