# 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 - Total Overhead Cost Variance ~ TOHCV

Is the actual total overhead cost incurred different from the total overhead cost absorbed?

The Total Overhead Cost Variance is the difference between the total overhead absorbed and the actual total overhead incurred. It represents the Under/Over Absorbed Total Overhead.

⇒ Total Overhead Cost Variance (TOHCV)

 = AbC − AC Absorbed Cost − Actual Cost

Actual cost incurred is ascertained from the financial information.

Where the actual total overhead cost incurred is not known, it can be calculated based on actual measure of the factor used for absorbing overheads like output, time worked etc. provided the related actual rate of overhead incurred is also known.

Actual Cost ~ AC

 = AO × AR/UO Or = AT × AR/UT Or = AD × AR/D

We restrict our discussion to the most common measures of activity, units of output, time worked for inputs and days for periods.

In problem solving absorbed cost may be
• provided as a calculated figure.
• obtained as the sum of absorbed variable cost and absorbed fixed cost

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

## Formula in useful forms

TOHCV = AbC − AC

### Absorption based on output units

Or = AO × (AbR/UO − AR/UO)

Actual Output × Difference between absorbed and actual Rates per unit output.

### Absorption based on input (time)

= AT × (AbR/UT − AR/UT)

Actual Time × Difference between budgeted and actual Rates per unit time

### Absorption based on periods (days)

= AD × (AbR/D − AR/D)

Actual Days × Difference between budgeted and actual Rates per day

## Note

• AbR/UO, AbR/UT, AbR/D in the above calculations pertains to total 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 TOHCV.

# Solution - (Assuming absorption is based on Output)

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) 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

60

6

4,800

25.625
20,500

2,050
26
22,360

49,200
86,100
1,35,300

66

1,23,000

=BR

=BR

=BR

In the absence of information to the contrary we assume

 AbR/UO(T) = BR/UO(T) = 60

Absorbed Total Overhead Cost ~ AC(T)

 = AO × AbR/UO(T) = 2,050 units × 60/unit = 1,23,000

 TOHCV = AbC − AC = 1,23,000 − 1,35,300 = − 12,300 [Adv]

## Alternatives

 TOHCV = AO × (AbR/UO − AR/UO) = 2,050 units × (60/unit − 66/unit) = 2,050 units × (− 6/unit) = − 12,300 [Adv]
(AO) =
 AO BO
=
 2,050 units 2,000 units
= 1.025
• ## Calculations based on input (time)

The absorbed overhead may be ascertained using the data relating to input.

Standard input (time) for actual output and the overhead absorption rate per unit input are required for such a calculation.

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
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(T) = BR/UT(T) = 6

Absorbed Total Overhead Cost ~ AbC(T)

 = ST(AO) × AbR/UT(T) = 20,500 hrs × 6/hr = 1,23,000
• ## Calculations based on periods (days)

The absorbed overhead may be ascertained using the data relating to periods, days in this case.

Standard periods (days) for actual output and the overhead absorption rate per unit period (day) are required for such a calculation.

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

In the absence of information to the contrary we assume

 AbR/D(T) = BR/D(T) = 4,800

Absorbed Total Overhead Cost ~ AbC(T)

 = SD(AO) × AbR/D(T) = 25.625 days × 4,800/day = 1,23,000

Building the working table with all the values needed and then using the formula based on values would be the simplest method to arrive at the value of the variance.

The method of absorption adopted and the method of calculation adopted would influence the calculation of the overhead absorbed only.

# Solution - (Assuming absorption is based on Input [time])

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

60

6

4,800
2,236
27.95

2,050
26
22,360

49,200
86,100
1,35,300

6.051

1,34,160

=BR

=BR

=BR
The actual rate per hour shown as 6.051 is an approximation of
 6,675 1,118

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

In the absence of information to the contrary we assume

 AbR/UT(T) = BR/UT(T) = 6/hr

Absorbed Total Overhead Cost ~ AC(T)

 = AO × AbR/UT(T) = 22,360 hrs × 6/hr = 1,34,160

 TOHCV = AbC − AC = 1,34,160 − 1,35,300 = − 1,140 [Adv]

## Alternatives

TOHCV = AT × (AbR/UT − AR/UT)
= 22,360 hrs × (6/hr −  6,675 1,118
/hr)
= 22,360 hrs × ( 6,708 − 6,765 1,118
/hr)
= 20 × (− 57)
(AT) =
 AT BT
=
 22,360 hrs 20,000 hrs
= 1.118
• ## Calculations based on output

The absorbed overhead may be ascertained using the data relating to output.

Standard output for actual input (time) and the overhead absorption rate per unit output are required for such a calculation.

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(T) = BR/UO(T) = 60

Absorbed Total Overhead Cost ~ AbC(T)

 = SO(AT) × AbR/UO(T) = 2,236 units × 60/unit = 1,34,160
• ## Calculations based on periods (days)

The absorbed overhead may be ascertained using the data relating to periods, days in this case.

Standard periods (days) for actual output and the overhead absorption rate per unit period (day) are required for such a calculation.

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

In the absence of information to the contrary we assume

 AbR/D(T) = BR/D(T) = 4,800

Absorbed Total Overhead Cost ~ AbC(T)

 = SD(AO) × AbR/D(T) = 27.95 days × 4,800/day = 1,34,160

Building the working table with all the values needed and then using the formula based on values would be the simplest method to arrive at the value of the variance.

The method of absorption adopted and the method of calculation adopted would influence the calculation of the overhead absorbed only.

# Solution - (Assuming absorption is based on Periods [days])

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)
1) Variable
2) Fixed
3) Total
(d1) ÷ (b)
(d2) ÷ (b)
(d3) ÷ (b)
2,000
25
20,000

40,000
80,000
1,20,000

60

6

4,800
2,080

20,800

2,050
26

49,200
86,100
1,35,300

5,203.85

1,24,800

=BR

=BR

=BR
The actual rate per hour shown as 5,203.85 is an approximation of
 67,650 13

In the absence of information to the contrary we assume

 AbR/UT(T) = BR/UT(T) = 4,800/day

Absorbed Total Overhead Cost ~ AC(T)

 = AD × AbR/D(T) = 26 days × 4,800/day = 1,24,800

 TOHCV = AbC − AC = 1,24,800 − 1,35,300 = − 10,500 [Adv]

## Alternatives

TOHCV = AD × (AbR/D − AR/D)
= 26 days × (4,800/day −  67,650 13
/hr)
= 26 days × ( 62,400 − 67,650 13
/hr)
= 2 × (− 5,250)
=
 26 days 25 days
= 1.04
• ## Calculations based on inputs (time)

The absorbed overhead may be ascertained using the data relating to input (time).

Standard input (time) for actual periods (days) and the overhead absorption rate per unit input are required for such a calculation.

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

In the absence of information to the contrary we assume

 AbR/UT(T) = BR/UT(T) = 6

Absorbed Total Overhead Cost ~ AbC(T)

 = ST(AD) × AbR/UT(T) = 20,800 hrs × 6/hr = 1,24,800
• ## Calculations based on output

The absorbed overhead may be ascertained using the data relating to output.

Standard output for actual periods (days) and the overhead absorption rate per unit output are required for such a calculation.

= 2,000 units × 1.04
= 2,080 units

In the absence of information to the contrary we assume

 AbR/UO(T) = BR/UO(T) = 60

Absorbed Total Overhead Cost ~ AbC(T)

 = SO(AD) × AbR/UO(T) = 2,080 units × 60/unit = 1,24,800

Building the working table with all the values needed and then using the formula based on values would be the simplest method to arrive at the value of the variance.

The method of absorption adopted and the method of calculation adopted would influence the calculation of the overhead absorbed only.

# Total Overhead Cost Variance - Miscellaneous Aspects

• ## Nature of Variance

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

• AbC ___ AC
• One that is relevant from these depending on the basis for absorption used

• AbR/UO ___ AR/UO
• AbR/UI ___ AR/UI
• AbR/UP ___ AR/UP

The variance would be

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

The following interpretations may be made

### No Variance

The incurred total overhead is the same as the absorbed total overhead

• ## Who is answerable for the Variance?

Since the Total Overhead Cost Variance represents the total difference on account of a number of factors it would not be possible to make someone or some department answerable for the variance.

This explains the reason for analysing the variance and segregating it into its constituent parts.

• ## Reasons for Variance not specific

The total overhead cost variance would only let us know that the actual total overhead cost is greater or lesser compared to the absorbed cost. It does not help us answer specific questions relating to the variance like, is it on account of the variation in the expenses incurred or the time taken for unit output etc.

Taking the data from the above illustration, we can notice that variance in total overhead cost may be on account of

• The activity achieved being different from the one planned in the budget

Working days - 26 actual to 25 budgeted.

Working Time - 22,360 actual to 20,000 budgeted.

• The actual overhead incurrence rate per unit time/output being different from the budgeted rate.

Overhead Rate per unit - Actual 66 to 60 budgeted.

Overhead Rate per unit time - Actual 6.05 to 6 budgeted.

• The rate at which the output has been achieved is different from the budgeted rate.

Time per unit output - 10.91 actual to 10 budgeted.

Standard Actual Absorbed
Budgeted for AO for AI for AP
A B C
a) Output (units)
b) Periods (Days)
c) Time (hrs)
...
g) Time/unit(hrs) (c) ÷ (a)
2,000
25
20,000

10

2,050
26
22,360

10.91
The actual time per unit shown as 10.91 is an approximation of  2,236 205

# Constituents of Total Overhead Cost Variance

## Aggregate Variance

The total overhead cost variance is always an aggregate of the variable overhead cost variance and the fixed overhead cost variance.

Since these two costs are of different nature, analysing the total overhead cost variance would amount to segregating the total cost into the variable and fixed parts and analysing the variances in them separately.

 TOHCV = AbC − AC = [AbC(V) + AbC(F)] − [AC(V) + AC(F)] = AbC(V) + AbC(F) − AC(V) − AC(F) = AbC(V) − AC(V) + AbC(F) − AC(F) = [AbC(V) − AC(V)] + [AbC(F) − AC(F)] = Variable Overhead Cost Variance + Fixed Overhead Cost Variance

# Formulae using Inter-relationships among Variances

1. TOHCV = VOHCV + FOHCV
2. TOHCV = VOHEXPV + VOHABSV + VOHEFFV + FOHEXV + FOHVV
3. TOHCV = VOHEXPV + VOHABSV + VOHEFFV + FOHEXV + FOHCAPV + FOHCALV + FOHEFV

## 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

a) VOHCV
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.