# Element wise cost per unit

Ascertaining the element cost per unit in evaluating various components of output is dependent on the presence or absence of opening and closing work in progress.
• ## No opening or closing work-in-progress

When there is neither opening nor closing work in progress

Element Cost per unit

=  Total Element Cost incurred in the current period Output units on which the cost is incurred

When there is no opening or closing work-in-progress we do not need the element wise cost per unit but just the total cost per unit for evaluating the various components of output.

Total Cost per unit =  Total Cost Total Units Output

Since the element wise cost per unit is not needed, there is no need to prepare the statement of equivalent production, statement of cost and statement of evaluation.

• ## only closing work-in-progress

When there is only closing work in progress

Element Cost per unit

=  Total Element Cost incurred in the current period Completed Output units + Equivalent Complete units of closing work-in-progress relating to the element

To ascertain the equivalent complete units of closing work-in-progress a statement of equivalent production is prepared. After that by preparing the statement of cost, the cost per unit of each element of cost is ascertained. Using this cost per unit, the values of various components of output are derived.

• ## both opening and closing work-in-progress

When there is opening work in progress, the fact that some of the cost in relation to the units of opening work in progress has already been spent in the previous period has to be taken into consideration in calculating the element wise cost per completed unit based on which the values of various components of output are evaluated.

There are two approaches to handling the previous period costs.

## Excluding Previous Period costs (FIFO Method)

The previous period costs are excluded and only the current period costs are considered for ascertaining the cost per completed unit.

Element Cost per unit

=  Total Element Cost incurred in the current period Equivalent complete units relating to element cost incurred on opening work-in-progress + Completed Output units started and completed in the current period + Equivalent Complete units of closing work-in-progress relating to the element

## Including Previous Period costs (Average Method)

The previous period costs are added up with the current period costs and the total cost is considered for ascertaining the cost per completed unit.

Element Cost per unit

=  Element cost included in the Opening work-in-progress + Total Element Cost incurred in the current period Equivalent complete units relating to element cost incurred on opening work-in-progress + Completed Output units started and completed in the current period + Equivalent Complete units of closing work-in-progress relating to the element
• ## only opening work-in-progress

The need for evaluating work-in-progress arises only when there is closing work in progress. The closing work-in-progress of a period becomes the opening work-in-progress for the subsequent period. Thus the opening work-in-progress is an asset which has already been evaluated in the previous period and needs no evaluation in the current period.

The value of opening work-in-progress is added up to the other costs incurred in the current period in arriving at the total cost.

Total Cost per unit =  Total Cost (including value of opening work-in-progress) Total Units Output (including opening work-in-progress units)

This total cost per unit would be the Normal cost of normal output per unit (NCNO/U) and is used in evaluating the various components of output as finished output, abnormal loss, abnormal gain etc.

### Element wise cost/unit not needed

When there is no need to evaluate closing work-in-progress, the element wise cost per unit is not needed for ascertaining the values of various components of output.

Since the element wise cost per unit is not needed, there is no need to prepare the statement of equivalent production, statement of cost and statement of evaluation.

# Valuation of work in progress - FIFO Method

When there are both opening and closing work-in-progress, there are two methods available for calculating the element cost per unit for the purpose of evaluating the components of output.

Under the FIFO (First in First Out) method for evaluation of components of cost, the previous period costs are excluded and only the current period costs are considered for finding out the element cost per completed unit.

The statement of equivalent production, statement of cost and statement of evaluation under the FIFO method would have the following formats.

### Statement of Equivalent Production

In preparing the statement of equivalent production, the output is seggregated into two as
1. Opening Work-in-progress Completed
2. Production started and completed in the current period
Statement of Equivalent Production
In Out Equivalent Units
Particulars Units Particulars Units Material Wages
%
Complete
Equivalent
Units
%
Complete
Equivalent
Units
Opening W-I-P
Input Introduced
2,300
12,000
Opening W-I-P Completed
Started & Completed
Closing W-I-P
2,300
10,000
2,000
70%1,61040%920
Totals 14,300 14,300 12,450

% completion relating to opening work in progress units completed during the current period would be the complementary of the % completion of opening work in progress with respect to the element

Eg : If Opening work-in-progress units 2,300 are 30% complete with regards to Materials and 60% complete with regards to Wages. They are 70% (100 − 30) and 40% (100 − 60) complete respectively with regards to Material and Wages in the current period.

### Statement of Cost

In preparing the statement of cost, only the current period cost has to be considered
Statement of Cost
Element of Cost Equivalent Units

(a)
Cost Incurred
(current period)
(b)
Cost/Unit

(b) ÷ (a)
Material
Wages
12,450 2,98,800 24
Total

### Statement of Evaluation

In preparing the statement of evaluation, the value of opening work-in-progress is added to the current period value of opening work-in-progress arrived at using the cost per unit and equivalent output units.
Statement of Evaluation
Component
Element of Cost
Equivalent Units
(a)
Cost/Unit
(b)
Total Cost
(a) × (b)
Value
a) Opening Work in Progress
Opening Balance
Material
Wages
b) Started & Completed
Material
Wages
1) Total Output
c) Closing Work in Progress
Material
Wages

1,610

24

42,000
38,640

Total Cost [42,000 + –]

### Cross Check

The total of the value column of the Statement of evalaution should be the same as the total cost column of the Statement of Cost plus the value of opening work in progress.

## Essential Data

To evaluate the components of output under FIFO method, the following information is essential.
• the total value of opening work-in-progress
• the element wise % completion of opening work-in-progress
In the absence of this information, finding the equivalent units relating to opening work in progress completed would not be possible and the total value of opening work in progress units in the statement of evaluation is not possible.

## Why called FIFO method?

Since the opening work in progress units are assumed to have been handled separately, it amounts to working on opening work-in-progress units first, completing them and then handling the inputs of the current period. Such a methodology is similar to the first in first out mechanism used for inventory handling and valuation. As such this method is called FIFO method.

The total cost for ascertaining the element cost per unit consists of only the current period cost. Thus the element cost per unit represents only the current period costs.

# Valuation of work in progress - Weighted Average Method

When there are both opening and closing work-in-progress, there are two methods available for calculating the element cost per unit for the purpose of evaluating the components of output.

Under the Weighted Average method for evaluation of components of cost, the previous period costs are added up to the current period costs and the total cost is considered for finding out the element cost per completed unit.

The statement of equivalent production, statement of cost and statement of evaluation under the weighted average method would have the following formats.

### Statement of Equivalent Production

In preparing the statement of equivalent production, no differentiation is made with regards to opening work in progress units completed and production started and completed in the current period.
Statement of Equivalent Production
In Out Equivalent Units
Particulars Units Particulars Units Material Wages
%
Complete
Equivalent
Units
%
Complete
Equivalent
Units
Opening W-I-P
Input Introduced
2,300
12,000
Completed
Closing W-I-P
12,300
2,000
100%12,300100%12,300
Totals 14,300 14,300 13,500

All completed units are considered to have been started and completed in the current period itself.

### Statement of Cost

In preparing the statement of cost, since the opening work-in-progress units are considered to have been started and completed in the current period itself, the cost incurred on them in the previous period has to be added to the cost incurred in the current period in arriving at the total cost considered for finding the element unit cost.
Statement of Cost
Element of Cost Equivalent Units
(a)
Cost Incurred Cost/Unit

(d) ÷ (a)
Previous
Period
(b)
Current
Period
(c)
Total
(d)
= (b) + (c)
Material
Wages
13,500 11,700 2,98,800 3,10,500 23
Total

### Statement of Evaluation

In preparing the statement of evaluation, we need to be conscious that the opening work in progress would not be separately evaluated as the output includes both the work-in-progress completed and the production started and completed in the current period.
Statement of Evaluation
Component
Element of Cost
Equivalent Units
(a)
Cost/Unit
(b)
Total Cost
(a) × (b)
Value
a) Completed Output
Material
Wages
b) Closing Work in Progress
Material
Wages

12,300

23

2,82,900

Total Cost

## Essential Data

To evaluate the components of output under Weighted Average method, the following information is essential.
• the element wise distribution of the value of opening work-in-progress
In the absence of this information, finding the total cost (previous period cost + current period cost) relating to each element in the statement of cost is not possible.

## Why called Average method?

The costs of the previous period included in the value of the opening work in progress are combined with the costs incurred in the current period in arriving at the total cost used for ascertaining the element cost per unit. Since the element cost per unit includes both the previous period costs and the current period costs, it is interpreted as being an average (or weighted average) of the costs of the two periods. As such this method is called the Weighted Average method.

# Illustration - Problem

Consider the following data relating to a process for the month of March 2007.
• 1,800 units were in process at the beginning valued at 83,200 made up of 38,400 of material cost, 24,000 of labour/labor cost and 20,800 of overhead expenditure.

These units were

1. 80% complete with regard to Direct Materials,
2. 40% complete with respect to Labour/Labor and
3. 60% complete with regard to Overhead Expenses
• 12,000 units of material were introduced into the process during the period.
• Total Material Cost incurred for the process is 2,11,680.
• Direct Wages incurred were - 2,73,240
• There were 2,400 units in process at the end of the period

These units were

1. 75% complete with regard to Direct Materials,
2. 50% complete with respect to Labour/Labor and
3. 30% complete with regard to Overhead Expenses
There were no losses in processing.

# Illustration - Solution - Working Notes

The process account filled with the information available from the problem

Process A a/c
Dr Cr
Particulars Quantity
(in Units)
Amount Particulars Quantity
(in Units)
Amount
To Balance b/d
To Direct Materials
To Labour/Labor
1,800
12,000
83,200
2,11,680
2,73,240
1,32,480
By Process A Stock a/c
By Process W-I-P a/c
 Total Input = Opening Work in Progress Units + Units Introduced = 1,800 units + 12,000 units = 13,800 units

Closing work-in-progress = 2,400 units

 Completed Production = Total Input − Closing work-in-progress = 13,800 units − 2,400 units = 11,400 units

# Illustration - Solution - FIFO Method

Statement of Equivalent Production
In Out Equivalent Units
Particulars Units Particulars Units Material Labor/Labour Overheads
%
Complete
Equivalent
Units
%
Complete
Equivalent
Units
%
Complete
Equivalent
Units
Opening W-I-P
Input Introduced
1,800
12,000
Opening W-I-P Completed
Started & Completed
Closing W-I-P
1,800
9,600
2,400
20%
100%
75%
360
9,600
1,800
60%
100%
50%
1,080
9,600
1,200
40%
100%
30%
720
9,600
720
Totals 13,800 13,800 11,760 11,880 11,040

Production Started and Completed in the current period

 = Total Production/Output − Opening Work-in-Progress Complete = 11,400 units − 1,800 units = 9,600 units

Element wise opening work-in-progress % completion in the current period

Element % Completion
Previous Period
(Opening)
(a)
Current Period
100 − (a)
Material
Labour/Labor
80%
40%
60%
20%
60%
40%

Units started and completed in the current period are 100% complete with regards to all elements and the closing work-in-progress is complete to the extent as given.

Statement of Cost
Element of Cost Equivalent Units

(a)
Cost Incurred
(current period)
(b)
Cost/Unit

(b) ÷ (a)
Material
Labour/Labor
11,760
11,880
11,040
2,11,680
2,73,240
1,32,480
18
23
12
Total 6,17,400 53
Statement of Evaluation
Component
Element of Cost
Equivalent Units
(a)
Cost/Unit
(b)
Total Cost
(a) × (b)
Value
a) Opening Work in Progress
Opening Balance
Material
Labour/Labor
b) Started & Completed
Material
Labour/Labor
1) Total Output
c) Closing Work in Progress
Material
Labour/Labor

360
1,080
720

9,600
9,600
9,600

1,800
1,200
720

18
23
12

18
23
12

18
23
12

83,200
6,480
24,840
8,640

1,72,800
2,20,800
1,15,200

32,400
27,600
8,640

1,23,160

5,08,800
6,31,960

68,640
Total Cost [83,200 + 6,17,400] 7,00,600

### Cross Checking for adjusting approximations

• Total of Total Cost column in Statement of Cost + Value of opening work-in-progress = 7,00,600 (6,17,400 + 83,200)
• Total of Value column in Statement of Evaluation = 7,00,600
Process A a/c
Dr Cr
Particulars Quantity
(in Units)
Amount Particulars Quantity
(in Units)
Amount
To Balance b/d
To Direct Materials
To Labour/Labor
1,800
12,000
83,200
2,11,680
2,73,240
1,32,480
By Process A Stock a/c
By Process W-I-P a/c
11,400
2,400
6,31,960
68,640
13,800 7,00,600 13,800 7,00,600

# Illustration - Solution - Weighted Average Method

Statement of Equivalent Production
In Out Equivalent Units
Particulars Units Particulars Units Material Labour/Labor Overheads
%
Complete
Equivalent
Units
%
Complete
Equivalent
Units
%
Complete
Equivalent
Units
Opening W-I-P
Input Introduced
1,800
12,000
Completed
Closing W-I-P
11,400
2,400
100%
75%
11,400
1,800
100%
50%
11,400
1,200
100%
30%
11,400
720
Totals 13,800 13,800 13,200 12,600 12,120

Units completed are 100% complete with regards to all elements and closing work-in-progress units are complete to the extent given in the problem.

Statement of Cost
Element of Cost Equivalent Units
(a)
Cost Incurred Cost/Unit

(d) ÷ (a)
Previous
Period
(b)
Current
Period
(c)
Total
(d)
= (b) + (c)
Material
Labour/Labor
13,200
12,600
12,120
38,400
24,000
20,800
2,11,680
2,73,240
1,32,480
2,50,080
2,97,240
1,53,280
18.9455
23.5905
12.6469
Total 83,200 6,17,400 7,00,600 55.1829
Statement of Evaluation
Component
Element of Cost
Equivalent Units
(a)
Cost/Unit
(b)
Total Cost
(a) × (b)
Value
a) Completed Output
Material
Labour/Labor
b) Closing Work in Progress
Material
Labour/Labor

11,400
11,400
11,400

1,800
1,200
720

18.9455
23.5905
12.6469

18.9455
23.5905
12.6469

2,15,979
2,68,932
1,44,175

34,102
28,309
9,106

6,29,084
6,29,086

71,516
71,517
Total Cost 7,00,600
7,00,603

### Cross Checking for adjusting approximations

• Sum of Total Cost column in Statement of Cost = 7,00,600
• Sum of Value column in Statement of Evaluation = 7,00,603
• A value of 3 is adjusted from the output and closing work-in-progress to adjust approximate values.
Process A a/c
Dr Cr
Particulars Quantity
(in Units)
Amount Particulars Quantity
(in Units)
Amount
To Balance b/d
To Direct Materials
To Labour/Labor
1,800
12,000
83,200
2,11,680
2,73,240
1,32,480
By Process A Stock a/c
By Process W-I-P a/c
11,400
2,400
6,29,084
71,516
13,800 7,00,600 13,800 7,00,600

# Which method to use? What's the difference?

Whether to use the FIFO method or the Weighted Average method for evaluation is the choice of the organisation. However, the actual possibility to choose a specific method is dependent on the availability of information relating to the opening work-in-progress.
• # FIFO Method

The essential data required is
• Total value of opening work-in-progress
• Element wise % completion with respect to opening work-in-progress

Eg : There are 12,000 units of opening work-in-progress units at a total value of 45,000 which are 80% complete with regard to Direct Materials, 40% complete with respect to Labour/Labor and 60% complete with regard to Overhead Expenses

• # Weighted Average Method

The essential data required is
• Element wise distribution of value of opening work-in-progress

Eg : 1,800 units were in process at the beginning valued at 83,200 made up of 38,400 of material cost, 24,000 of labour/labor cost and 20,800 of overhead expenditure.

In problem solving, in the absence of specific instruction regarding the method to use and the information required for both the methods is available, we can choose any method for evaluation.

# Difference

Apart from the difference in the workings of the two methods, the difference would lie in the element wise cost per unit arrived at and the values of output components.

The ultimate difference would be in the value of the various components which are evaluated in the statement of evaluation. These are the values that are present on the credit side of the process account.

Considering the illustration worked out above, we can notice differences in these:

Particulars FIFO Method AVERAGE Method
Cost per unit (from the statement of cost)
Material
Labour/Labor
Value of Completed Production
Value of Closing Work in Progress

18
23
12
6,31,960
68,640

18.9455
23.5905
12.6469
6,29,084
71,516

# Only Open Work-in-Progress - Illustration

## Problem

Consider the following cost data of an organisation relating to a process for the month of March 2007.
• 1,800 units were in process at the beginning valued at 83,200 made up of 38,400 of material cost, 24,000 of labour/labor cost and 20,800 of overhead expenditure.

These units were

1. 80% complete with regard to Direct Materials,
2. 40% complete with respect to Labour/Labor and
3. 60% complete with regard to Overhead Expenses
• 6,000 units of material were introduced into the process at a total cost of 2,25,000.
• Direct Wages incurred for the process - 1,84,000
There was no work-in-progress or any other stocks at the end of the period. There were no losses in processing.

## Solution

Process A a/c
Dr Cr
Particulars Quantity
(in Units)
Amount Particulars Quantity
(in Units)
Amount
To Balance b/d
To Direct Materials
To Labour/Labor
1,800
6,000
83,200
2,25,000
1,84,000
92,800
By Finished Production
7,800
5,85,000
7,800 5,85,000   7,800 5,85,000
Processing
Particulars Quantity Cost Cost/Unit
Opening Work-in-Progress
Materials
1,800
6,000
83,200
2,25,000
Input Processed (IP)
+ Other Costs
Labour/Labor
7,800 3,08,200

1,84,000
92,800
Total (IP | TC) 7,800 5,85,000 75
Normal (NO | NC | NCNO/U)
− Actual Output
7,800
7,800
5,85,000
5,85,000
75
Abnormal Loss(+)/Gain(−)
• Normal Cost of Normal Output per unit  NCNO/U = $\frac{\mathrm{NC}}{\mathrm{NO}}$
• Actual output (7,800 × 75) is valued at NCNO/U
Author : The Edifier