# 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 Efficiency Variance ~ FOHEFFV

Is the output derived from the actual input different from the standard output for the actual input?

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

⇒ Fixed Overhead Efficiency Variance (FOHEFFV)

 = SC(AO) − SC(AI) Standard Cost for Actual Output − Standard Cost for Actual Input

## Standard Cost for Actual Output (Fixed Overhead)

Standard Cost for Actual Output ~ SC(AO)

= BC ×
 AO BO
Or = AO × BR/UO
Or = SI(AO) × BR/UI
Or = SP(AO) × BR/UP

## 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

## Formula in useful forms

FOHEFV = SC(AO) − SC(AI)

Standard Cost for Actual Output − Standard Cost for Actual Input

Or = BC × (
 AO BO
 AI BI
)

Budgeted Cost × Difference between proportion of actual output to budgeted output and proportion of actual input to budgeted input

Or = [AO − SO(AI)] × BR/UO

Difference between actual output and standard output for actual input × Budgeted Rate per unit output

Or = [SI(AO) − AI] × BR/UI

Difference between standard input for actual output and actual input × Budgeted Rate per unit input

Or = [SP(AO) − SP(AI)] × BR/UP

Difference between standard periods for actual output and standard periods for actual input × Budgeted Rate per unit period

## Note

• 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 FOHEFV.

## Taking time for input and days for periods

FOHEFV = SC(AO) − SC(AT)
Or = BC × (
 AO BO
 AT BT
)
Or = [AO − SO(AT)] × BR/UO
Or = [ST(AO) − AT] × BR/UT
Or = [SD(AO) − SD(AT)] × BR/D

# Formulae - When Absorption variance is not calculated

Calculation of Absorption variance can be avoided where the absorption is being done based on output units and the budgeted rate is the absorption rate. In such a case, in the formula for calculating efficiency variance, Absorbed Cost (AbC) takes the place of Standard Cost for Actual output SC(AO).

This will only affect the names we use for the terms in the formula, since in such a case the AbC = SC(AO).

The Fixed Overhead Efficiency Variance is the difference between the absorbed cost and the standard cost for actual input.

⇒ Fixed Overhead Efficiency Variance (FOHEFV)

 = AbC − SC(AI) Absorbed Cost − Standard Cost for actual input

• ### Absorption based on output (units)

Absorbed Cost ~ AbC

 = AO × AbR/UO Or = SI(AO) × AbR/UI Or = SP(AO) × AbR/UP

Since AbR = BR

Absorbed Cost ~ AbC

= AO × BR/UO
= BC ×  AO BO
[Since BR/UO =  BC BO
]
Or = SI(AO) × BR/UI
Or = SP(AO) × BR/UP

## 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

## Formula in useful forms

FOHEFV = AbC − SC(AI)
Or = BC × (
 AO BO
 AI BI
)
Or = [AO − SO(AI)] × BR/UO
Or = [SI(AO) − AI] × BR/UI
Or = [SP(AO) − SP(AI)] × BR/UP

The only difference is the term SC(AO) being replaced by AbC in the formula using costs. All other formulae forms are the same.

## Taking time for input and days for periods

FOHEFV = AbC − SC(AT)
Or = BC × (
 AO BO
 AT BT
)
Or = [AO − SO(AT)] × BR/UO
Or = [ST(AO) − AT] × BR/UT
Or = [SD(AO) − SD(AT)] × BR/D

# Solution - Working Notes

Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
I) Factor 1.025 1.118 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)
1) Variable
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

42,000

2,236
27.95

89,440

2,080

20,800

2,050
26
22,360

49,200
86,100
1,35,300

42,000

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

The following calculations may be made directly in the working table thus eliminating these workings.

Factor = Actual Data ÷ Standard/Budgeted Data

Relevant value = Standard/Budgeted Data × Factor

(AO) =
 AO BO
=
 2,050 units 2,000 units
= 1.025
SC(AO) = SC ×
 AO BO
= BC × 1.025
 SC(AO)(F) = BC(F) × 1.025 = 80,000 × 1.025 = 82,000
 ST(AO) = BT × 1.025 = 20,000 hrs × 1.025 = 20,500 hrs
 SD(AO) = BD × 1.025 = 25 days × 1.025 = 25.625 days
(AI) = (AT)
=
 AT BT
=
 22,360 hrs 20,000 hrs
= 1.118
SC(AI) = SC(AT)
= BC ×
 AT BT
= BC × 1.118
 SC(AT)(F) = BC(F) × 1.118 = 80,000 × 1.118 = 89,440
 SO(AI) = SO(AT) = BO × 1.118 = 2,000 units × 1.118 = 2,236 units
 SD(AT) = BD × 1.118 = 25 days × 1.118 = 27.95 days
=
=
 26 days 25 days
= 1.04
 SO(AP) = SO(AD) = BO × 1.04 = 2,000 units × 1.04 = 2,080 units
 ST(AP) = ST(AD) = BT × 1.04 = 2,000 hrs × 1.04 = 20,800 hrs

## When not using Absorption Variance

Overheads are absorbed on output basis and BR/UO is the AbR/UO
 AbR/UO = BR/UO = 20/unit
 AbC = AO × AbR/UO = 2,050 units × 40/unit = 82,000

# Solution - (all cases)

Since the formula for this variance does not involve absorbed overhead, the basis of absorption of overhead is not a factor that influences the calculation of this variance.

 FOHEFV = SC(AO) − SC(AI) = SC(AO) − SC(AT) = 82,000 − 89,440 = − 7,440 [Adv]

## When not using Absorption Variance

The term AbC takes the place of SC(AO).

 FOHEFV = AbC − SC(AI) = AbC − SC(AT) = 82,000 − 89,440 = − 7,440 [Adv]

The alternative formulae would be the same in both the cases.

## Alternatives

FOHEFV = BC × ( AO BO
 AI BI
)
= BC × ( AO BO
−  AT BT
)
= 40,000 × (1.025 − 1.118)
= 40,000 × (− 0.093)

 FOHEFV = [AO − SO(AI)] × BR/UO = [AO − SO(AT)] × BR/UO = (2,050 units − 2,236 units) × 40/unit = − 186 units × 40/unit = − 7,440 [Adv]

 FOHEFV = [SI(AO) − AI] × BR/UT = [ST(AO) − AT] × BR/UT = (20,500 hrs − 22,360 hrs) × 4/hr = − 1,860 hrs × 4/hr = − 7,440 [Adv]

 FOHEFV = [SP(AO) − SP(AI)] × BR/UP = [SD(AO) − SD(AT)] × BR/D = (25.625 days − 27.95 days) × 3,200/day = − 2.325 days × 3,200/day = − 7,440 [Adv]

# Fixed Overhead Efficiency Variance - Miscellaneous Aspects

• ## Nature of Variance

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

• SC(AO) ___ SC(AI)
•  AO BO
___  AI BI
• AO ___ SO(AI)
• SI(AO) ___ AI
• SP(AO) ___ SP(AI)

The variance would be

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

The following interpretations may be made

### No Variance

An output equal to the standard output for the input used is achieved.

### Favourable/Favorable

An output greater than the standard output for the input used is achieved. The value of the variance indicates the gain on account of such a variation.

An output lesser than the standard output for the input used is achieved. The value of the variance indicates the loss on account of such a variation.
• ## Who is answerable for the Variance?

Since this variance is on account of the utilisation of the input resources for achieving the output, the people or department responsible for production operations would be answerable for this variance.

# Formulae using Inter-relationships among Variances

1. FOHEFFV = FOHVOLV − FOHABSV − FOHCALV − FOHCAPV

## Verification

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

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

Author : The Edifier
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