# Evaluating Work-in-Progress requires Cost/unit data

The cost of a product is made up costs of various elements present in the cost like material, labour/labor and overheads.

We will be able to ascertain the value of work-in-progress if the following data is available.

• cost of each element per unit
• percentage completion of work-in-progress with respect to each element
• number of units of work-in-progress

With this data available there are two ways the value of work in progress can be ascertained

1. By evaluating the per unit expenditure on work in progress units with respect to each element
Elements of Cost Total
Expenses
a) Complete Cost (per unit)
b) % Completion
c) Incurred Cost (per unit) (a) × (b)
d) Work-in-Progress (units)
e) Total Cost (c) × (d)
70
100%
70
2,100
1,47,000
50
60%
30
2,100
63,000
20
75%
15
2,100
31,500
140

115
2,100
2,41,500
2. By converting the work-in-progress units into their equivalent complete units
W-I-P Units Percent (%)
Complete
Equivalent
Complete Units
Cost Per
Completed Unit
Total Cost
a) Material
b) Labour/Labor
2,100
2,100
2,100
100%
60%
75%
2,100
1,260
1,575
70
50
20
1,47,000
63,000
31,500
d) Total 2,100 2,41,500

In both these we need the cost per unit of each element of cost to arrive at the value of work-in-progress.

# Absence of Cost per unit data

The cost incurred per unit with respect to each element of cost is something that is derived through calculations based on the data relating to the cost incurred. It is not a figure that is readily available.
The relation, Cost per unit =
 Total Cost Total Units Processed/Output
holds only in case of completed production and not when the units processed is a mix of completed output and work in progress units.

The cost data available regarding a process would be in relation to the total expenditure incurred on both the completed units and the units in work-in-progress together. If the cost data is capable of being segregated into cost incurred on completed units and cost incurred on work in progress units, then the cost incurred on the work in progress units would itself form the value of work in progress units.

Therefore, in process cost accounting, the first task in evaluating the value of closing work-in-progress is to find out an estimate of the cost per unit of completed production based on the cost data available in relation to the process.

# Illustration

Consider the following cost data of an organisation relating to a process for the month of March 2007.
• 10,000 units of material were introduced into the process at a total cost of 2,63,200.
• Direct Wages incurred for the process - 1,14,800
• Production completed during the month was of 7,000 units.
• 3,000 units were in process (partially completed) as on 31st March.

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

There were no stocks at the beginning of the month. There were no losses in processing.

# Finding the cost per unit

The following cost data is made use of in finding the cost per unit of completed production
• quantity of completed units
• quantity of work-in-progress units
• percentage completion of the work-in-progress units with respect to each element of cost
• expenditure incurred on each element of cost

# Material Cost per unit

The total cost incurred 2,63,200

 = Expenditure incurred on 7,000 units of completed production + Expenditure incurred on 3,000 units of work-in-progress = 7,000 units × Full Cost per unit + 3,000 units × 80% of Full Cost per unit = 7,000 units × Full Cost per unit + 3,000 units × 80% × Full Cost per unit = 7,000 units × Full Cost per unit + 2,400 units × Full Cost per unit 3,000 units × 80% = 2,400 units (Converting Work-in-Progress units to equivalent complete units) = 9,400 units × Full Cost per unit = Expenditure incurred on 9,400 units of completed production

⇒ Material Cost per unit

=
 Expenditure incurred on 9,400 units of completed production 9,400 units
=
 Total Cost Equivalent Completed Units
=
 2,63,200 9,400 units
= 28/unit

# Labour/Labor Cost per unit

The total cost incurred 1,14,800

 = Expenditure incurred on 7,000 units of completed production + Expenditure incurred on 3,000 units of work-in-progress = 7,000 units × Full Cost per unit + 3,000 units × 40% of Full Cost per unit = 7,000 units × Full Cost per unit + 3,000 units × 40% × Full Cost per unit = 7,000 units × Full Cost per unit + 1,200 units × Full Cost per unit 3,000 units × 40% = 1,200 units (Converting Work-in-Progress units to equivalent complete units) = 8,200 units × Full Cost per unit = Expenditure incurred on 8,200 units of completed production

⇒ Labour/Labor Cost per unit

=
 Expenditure incurred on 8,200 units of completed production 8,200 units
=
 Total Cost Equivalent Completed Units
=
 1,14,800 8,200 units
= 14/unit

The total cost incurred 2,11,200

 = Expenditure incurred on 7,000 units of completed production + Expenditure incurred on 3,000 units of work-in-progress = 7,000 units × Full Cost per unit + 3,000 units × 60% of Full Cost per unit = 7,000 units × Full Cost per unit + 3,000 units × 60% × Full Cost per unit = 7,000 units × Full Cost per unit + 1,800 units × Full Cost per unit 3,000 units × 60% = 1,800 units (Converting the Work-in-Progress units to equivalent complete units) = 8,800 units × Full Cost per unit

=
 2,11,200 8,800 units
= 24/unit

## Cost per unit is an estimate

Since the % completion of work in progress is an estimate, the cost per unit of completed production derived using that data would also be an approximate figure i.e. an estimate.

The above calculations presented in the form of a statement would be as below.

Elements of Cost Total
Expenses
a) Total Cost incurred
b) Complete Production units
c) Work-in-Progress units
d) Work-in-Progress % complete
e) W-i-P Equivalent Complete units (c) × (d)
f) Total Complete units (b) + (e)
e) Cost per unit (a) ÷ (f)
2,63,200
7,000
3,000
80%
2,400
9,400
28
1,14,800
7,000
3,000
40%
1,200
8,200
14
2,11,200
7,000
3,000
60%
1,800
8,800
24
140
7,000
3,000

66

The total process of finding the cost per unit of completed production is segregated into two stages by preparing two separate statements.

• ## Statement of Equivalent Production (Or) Equivalent Production Statement

This statement gives the number of completed units on which the total expenditure might be considered to have been incurred.
• ## Statement of Cost

This is a statement that gives the cost per unit of each element based on the total expenditure incurred and the number of completed units on which the expenditure might be considered to be incurred.

# Statement of Equivalent Production

This statement is used to derive the information relating to the number of completed units on which the expenditure might be considered to have been incurred.
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

Totals

## Accommodating additional Elements of Cost

If there are more elements of cost involved additional columns under the head Equivalent Units should be provided for the same.
Statement of Equivalent Production
In Out Equivalent Units
Particulars Units Particulars Units Primary
Material
Secondary
Material
%
Complete
Equivalent
Units
%
Complete
Equivalent
Units
%
Complete
Equivalent
Units
%
Complete
Equivalent
Units

Totals

## Illustration

The Equivalent production statement relating to the data in the above illustration would be:
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
Introduced 10,000 Completed
Work-in-Progress
7,000
3,000
100%
80%
7,000
2,400
100%
40%
7,000
1,200
100%
60%
7,000
1,800
Totals 10,000 10,000 9,400 8,200 8,800

## Relevance to Process a/c

The In and Out columns are an equivalent of the process account with only the unit columns shown.
Process A a/c
Dr Cr
Particulars Quantity
(in Units)
Amount Particulars Quantity
(in Units)
Amount
To Primary Material
To Direct Wages
10,000
2,63,200
1,14,800
2,11,200
By Process B a/c
By Process A W-i-P a/c
7,000
3,000
??
??
10,000 5,89,200 10,000 5,89,200

## % Completion of various components of output

Output Component % Complete
(with respect to all elements of cost)
Completed Production
Closing Work-in-Progress
Normal Loss
Abnormal Loss
Abnormal Gain
100%
As Given
0%
As Given (100% otherwise)
100%

# Statement of Cost

The statement of cost is prepared to ascertain the cost per unit of completed production with respect to each element of cost.
Statement of Cost
Element of Cost Equivalent Units Total Cost
(current period)
Cost/unit
(completed production)
(a) (b) (b) ÷ (a)

Totals

## Illustration

The Statement of Cost relating to the data in the above illustration would be:
Statement of Cost
Element of Cost Equivalent Units Total Cost
(current period)
Cost/unit
(completed production)
(a) (b) (b) ÷ (a)
Materials
Labour/Labor
9,400
8,200
8,800
2,63,200
1,14,800
2,11,200
28
14
24
Totals 5,89,200 62

The data relating to equivalent units is derived from the statement of equivalent production. The cost data is derived from the information provided.

## Normal Cost of Normal Output per unit

The cost per unit arrived at in the Statement of Cost represents the Normal Cost of Normal Output per unit.

When there is closing work-in-progress, we have the per unit cost of each element of cost available unlike in other cases where we come across only the per unit total cost.

## Adjustment for Normal Loss realisation

When there are no losses,
Normal Cost of Normal Output/unit
=
 Total Cost Total Output
Where there is normal loss
=
 Normal Cost Normal Output
=
 Total Cost − Normal Loss Realisation Input Units − Normal Loss Units

When there is normal loss, the cost that is considered for calculating the cost per unit would be the normal cost which would be the total cost reduced by the normal loss realisation.

Since we calculate the cost per unit for each element of cost, the normal loss realisation has to be deducted from the cost relating to one of the elements of cost. Deducting it from Material cost would be appropriate. We use the reduced cost in finding out the cost per unit.

# Statement of Evaluation

The last step in the process of finding the value of closing work-in-progress is evaluation.

This is done based on the data available in the statement of equivalent production and the statement of cost.

Where, there is closing work-in-progress, the evaluation of various output elements like finished product, closing work-in-progress as well as others like normal loss, abnormal loss, abnormal gain evaluated in the statement of evaluation itself.

Statement of Evaluation
Component to be Evaluated Equivalent Units Cost Per unit Total Cost Value
a) Finished Output
Material
Labour/Labor
b) Normal Loss
Material
Labour/Labor
c) Abnormal Loss
Material
Labour/Labor
d) Closing Work in Progress
Material
Labour/Labor
e) Closing Finished Goods
Material
Labour/Labor

Total Cost

### Cross Check for adjusting approximation

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. This would help to make adjustments to approximations.

## Illustration

The Statement of Cost relating to the data in the above illustration would be:
Statement of Evaluation
Component to be Evaluated Equivalent Units
(a)
Cost/Unit
(b)
Total Cost
(a) × (b)
Value
a) Finished Output
Material
Labour/Labor
b) Closing Work in Progress
Material
Labour/Labor

7,000
7,000
7,000

2,400
1,200
1,800

28
14
24

28
14
24

1,96,000
98,000
1,68,000

67,200
16,800
43,200

4,62,000

1,27,200
Total Cost 5,89,200

ΣValue column (statement of evaluation) = ΣTotalCost column (statement of cost) = 5,89,200

## Relevance to Process a/c

The values arrived at in the Statement of Evaluation form the missing values that we derive through calculations.
Process A a/c
Dr Cr
Particulars Quantity
(in Units)
Amount Particulars Quantity
(in Units)
Amount
To Primary Material
To Direct Wages
10,000
2,63,200
1,14,800
2,11,200
By Process B a/c
By Process W-i-P a/c
7,000
3,000
4,62,000
1,27,200
10,000 5,89,200   10,000 5,89,200

The values recorded on the credit should always be derived through calculations. Where there is closing work-in-progress, these values are fetched from the statement of evaluation. Where there is no closing work-in-progress these are fetched from the Input, Processing and Output working notes.

## Is the principle for valuation being followed?

The principle for valuation states that Normal Loss is valued at its net realisable price and all others are valued at the Normal Cost of Normal Output per unit. This holds and is followed even when there is closing work in progress. We can notice this in the evaluation statement where the normal cost of normal output per unit with respect to each element is what is considered for evaluating the various components.
Author : The Edifier