The concept of equivalent units.

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The concept of equivalent units

Equivalent Units

When units are partly completed at the end of a period (and hence there is closing work in progress), it is necessary to calculate the equivalent units of production in order to determine the cost of a completed unit. 

It would be unfair to allocate a full unit cost to part-process units so we need to use the concept of equivalent units.

Equivalent units are notional whole units which represent incomplete work, and which are used to apportion costs between work in process and completed output.

Closing work in progress units become opening work in progress units in the next accounting period.

Illustration

At the end of a process, there were 100 units that were 50% complete.

What are the equivalent units?

Solution

100 units x 50% = 50 E.U.

Illustration

Finished Goods 20,000 units valued at $800,000
Closing WIP 4,000 units valued at $120,000

What is the % completion of the Closing WIP?

Solution

Value of a finished unit:
800,000 / 20,000 = $40

Value of 1 Closing WIP unit:
120,000 / 4,000 = $30

% completion = 30/40 = 75%

Different degrees of completion

Since material is input at the start of the process, it is only the addition of labour and overheads that will be incomplete at the end of the period. 

This means that material cost should be spread over all units but conversion costs should be spread over the equivalent units.

Illustration

Finished goods 20,000 units
Closing WIP 5,000 (70%) for conversion cost

Conversion cost $150,000

What is the conversion cost per E.U?

Solution

For conversion cost

20,000 units are finished and (5,000 units are 70% finished) = 23,500 E.U.
 
Cost per E.U. for conversion = $150,000 / 23,500 = $6.38

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