Process Costing: Equivalent Units and Work-in-Progress

A process never stops. At the end of any month there are units that have been started but are not finished. Those units have used some of the materials and some of the work, but not all of it, so they should carry only part of a finished unit’s cost.

The idea that makes this fair is the equivalent unit: a way of counting part-finished units as if they were whole ones.

This topic shows how to cost closing work-in-progress, how to deal with opening work-in-progress using the weighted average method and the first in, first out (FIFO) method, and how to combine all of this with normal loss, abnormal loss and scrap. The method is always the same three-stage layout, so once you can set it out cleanly, every variation becomes a matter of filling in a different table.

Equivalent units

An equivalent unit means “equal to one finished unit”. Part-finished units are converted into the number of whole units that would have taken the same amount of work.

• 200 units that are 50% complete = 200 × 50% = 100 equivalent units.
• 400 units that are 20% complete = 400 × 20% = 80 equivalent units.

Costs are then shared between finished units and unfinished units by calculating a cost per equivalent unit.

Different stages of completion for different costs

Unfinished units are often complete to different degrees for different inputs. If all materials go in at the start of the process, every unit in work-in-progress is 100% complete for materials. But conversion costs (labour and overhead) are added gradually, so the same units may be only 40% complete for conversion.

Therefore the equivalent units of materials differ from the equivalent units of conversion, and a separate cost per equivalent unit is found for each.

The three-stage method

1. Statement of equivalent units. For finished output and for closing work-in-progress (and any abnormal loss), calculate equivalent units for materials and for conversion.
2. Statement of cost per equivalent unit. Divide the costs of each type by its equivalent units.
3. Statement of evaluation. Multiply equivalent units by the cost per equivalent unit to value finished goods, closing work-in-progress and losses. Then complete the process account.

Closing work-in-progress with no opening stock and no losses

A process takes in 6,000 units at the start of the month. 5,200 are completed and 800 remain in progress, 100% complete for materials and 50% complete for conversion. Materials cost ₦36,000 and conversion costs are ₦22,400.

Each unfinished unit carries ₦6 of materials and ₦4 × 0.5 = ₦2 of conversion, a cost of ₦8. A finished unit costs ₦10.

Opening work-in-progress

When there is opening work-in-progress, the debit side of the account has two kinds of cost: costs brought forward from last period, and costs for this period. The accounting policy decides how to treat them. There are two methods: weighted average and FIFO.

The data for both methods

Opening work-in-progress is 1,000 units, 100% complete for materials and 40% complete for conversion, valued at materials ₦5,400 and conversion ₦1,800. During the month 5,000 units are put in. 4,600 units are completed, and 1,400 are in closing work-in-progress (100% materials, 50% conversion). Costs in the month are materials ₦30,600 and conversion ₦19,400. (Check: 1,000 + 5,000 = 6,000 = 4,600 + 1,400.)

Method 1: weighted average

All units produced in the period and closing units are valued at the same average cost per equivalent unit. The opening work-in-progress costs are pooled with current costs. Equivalent units are based on units finished in the period (whenever they were started) and units in closing work-in-progress.

Evaluation: Finished goods 4,600 × ₦10 = ₦46,000. Closing WIP: materials 1,400 × ₦6 = ₦8,400; conversion 700 × ₦4 = ₦2,800; total ₦11,200. Total = ₦57,200, which equals the opening WIP ₦7,200 plus the month’s costs ₦50,000. ✓

Summary of weighted average: total cost = opening WIP cost + costs in the period. Total equivalent units = units finished + equivalent units in closing WIP. Cost per equivalent unit = total cost ÷ total equivalent units.

Method 2: FIFO

FIFO assumes the opening work-in-progress is the first to be finished. Its cost is its value at the start of the period plus the cost of completing it this period. The equivalent units of work done this period are:

• the work needed to complete the opening work-in-progress (the part not done last period);
• the units started and finished this period (finished output minus the opening WIP units), each with a full equivalent unit of materials and conversion; and
• the equivalent units in closing work-in-progress.

Cost per equivalent unit uses current-period costs only: materials ₦30,600 ÷ 5,000 = ₦6.12; conversion ₦19,400 ÷ 4,900 = ₦3.9592.

FIFO and weighted average give different values for finished goods (₦45,860.57 against ₦46,000) and for closing work-in-progress (₦11,339.43 against ₦11,200). Both total ₦57,200. FIFO is considered more accurate for control, because it separates last period’s costs from this period’s, while weighted average is simpler.

Work-in-progress with losses

Examination questions often combine work-in-progress and losses. The following conventions apply.

• Scrap value of normal loss is deducted from the materials cost. The scrap really reflects both materials and conversion, but the usual convention is to offset it against materials only.
• Normal loss units are left out of the equivalent units.
• Abnormal loss units are costed like good production, so the equivalent units of abnormal loss are included in the total equivalent units. If inspection happens when units are 100% complete, abnormal loss has full materials and full conversion. If inspection happens earlier, count conversion only to the stage reached.
• Draw up a physical units working first: input (plus opening WIP) − normal loss − completed − closing WIP = abnormal loss (or gain, if negative).

Closing WIP and losses (no opening stock)

Input 4,000 units. Normal loss 10% of input (400 units) scrapped at ₦1. Completed 3,000 units. Closing WIP 500 units (100% materials, 60% conversion). Costs: materials ₦22,000; conversion ₦6,800.

• Physical units.
  4,000 − 400 normal loss = 3,600 expected.
  Completed 3,000 + closing WIP 500 = 3,500.
  So abnormal loss = 100 units (assumed 100% complete).
• Equivalent units.
  materials = 3,000 + 500 + 100 = 3,600.
  Conversion = 3,000 + 300 + 100 = 3,400.
• Materials net of scrap.
  ₦22,000 − (400 × ₦1 = ₦400) = ₦21,600.
  Cost per equivalent unit: materials ₦21,600 ÷ 3,600 = ₦6
  conversion ₦6,800 ÷ 3,400 = ₦2.
• Valuation.
  finished 3,000 × ₦8 = ₦24,000.
  Closing WIP: 500 × ₦6 + 300 × ₦2 = ₦3,000 + ₦600 = ₦3,600.
  Abnormal loss 100 × ₦8 = ₦800.
  Normal loss ₦400.
  Total = ₦28,800 = ₦22,000 + ₦6,800. ✓

Opening WIP and losses: weighted average

Opening WIP 800 units (100% materials, 50% conversion) valued at materials ₦4,800 and conversion ₦1,600. Input in the month 4,200 units. Normal loss 5% of input (210 units) at ₦2 scrap. Completed 3,900 units. Closing WIP 700 units (100% materials, 60% conversion). Costs for the month: materials ₦33,940; conversion ₦16,440.

• Physical units.
  800 + 4,200 = 5,000.
  Less normal loss 210, completed 3,900 and closing WIP 700 leaves abnormal loss of 190 units.
• Equivalent units.
  materials = 3,900 + 700 + 190 = 4,790.
  Conversion = 3,900 + 420 + 190 = 4,510.
• Materials cost.
  ₦4,800 + ₦33,940 − scrap (210 × ₦2 = ₦420) = ₦38,320.
  Per equivalent unit = ₦38,320 ÷ 4,790 = ₦8.
  Conversion cost = ₦1,600 + ₦16,440 = ₦18,040.
  Per equivalent unit = ₦18,040 ÷ 4,510 = ₦4.
• Valuation.
  finished 3,900 × ₦12 = ₦46,800.
  Closing WIP: 700 × ₦8 + 420 × ₦4 = ₦5,600 + ₦1,680 = ₦7,280.
  Abnormal loss 190 × ₦12 = ₦2,280.
  Normal loss ₦420.
  Total = ₦56,780 = opening ₦6,400 + month’s costs ₦50,380. ✓

The ideas in more depth

Why not simply divide by units?

If you ignored work-in-progress and divided the total cost by finished units, finished goods would carry the cost of the unfinished ones. If you divided by all units, whether finished or not, work-in-progress would carry the cost of a whole unit. Equivalent units fix both errors by counting the work done.

Choosing the completion percentages

Percentages differ by input. Materials added at the start: 100% for all units in progress. Materials added at the end: 0% for work-in-progress. Conversion costs, spread through the process: about half way, or as stated. Read each question for where each input is added, and for the stage of inspection when losses are tested.

Ignoring equivalent units of normal loss

Normal loss units are not counted as equivalent units, because they are not an output that will be sold (other than at scrap value). If they were counted, equivalent units would rise and the cost per unit would fall, understating the cost of good output.

Which method to use

The question states the method. If it does not, use weighted average, which is simpler. Both methods must produce a total value of finished goods, closing stock and losses equal to the total of opening WIP and costs added. Check this at the end of every question.

Common layout

Set out five items, in order: (1) physical units working; (2) equivalent units statement; (3) cost per equivalent unit; (4) valuation; (5) the process account, with quantities and values. Marks are awarded for each statement.

Worked example: both methods on one set of data

1. Check units.
   600 + 3,400 = 4,000 = 2,900 + 1,100. ✓
2. (a) Weighted average.
   Equivalent units: materials = 2,900 + 1,100 = 4,000
   conversion = 2,900 + (1,100 × 40% = 440) = 3,340.
   Total costs: materials ₦3,000 + ₦21,000 = ₦24,000
   conversion ₦900 + ₦9,120 = ₦10,020.
   Cost per equivalent unit: materials ₦6; conversion ₦3.
   Finished goods = 2,900 × ₦9 = ₦26,100.
   Closing WIP = (1,100 × ₦6) + (440 × ₦3) = ₦6,600 + ₦1,320 = ₦7,920.
   Total = ₦34,020. ✓
3. (b) FIFO.
   Equivalent units: materials = 0 (opening) + 2,300 (started and finished: 2,900 − 600) + 1,100 = 3,400.
   Conversion = 300 (50% of 600) + 2,300 + 440 = 3,040.
   Current costs only: materials ₦21,000 ÷ 3,400 = ₦6.1765
   conversion ₦9,120 ÷ 3,040 = ₦3.
4. FIFO valuation.
   Opening WIP: ₦3,900 + 300 × ₦3 = ₦4,800.
   Started and finished: 2,300 × (₦6.1765 + ₦3) = ₦21,105.88.
   Finished output = ₦25,905.88.
   Closing WIP: 1,100 × ₦6.1765 = ₦6,794.12 plus 440 × ₦3 = ₦1,320, which is ₦8,114.12.
   Total = ₦34,020. ✓

Equivalent units in a second process

When the output of Process 1 passes to Process 2, it arrives as a transferred-in cost. For equivalent units, transferred-in material is always 100% complete in Process 2 (it arrived finished from the previous process), so work-in-progress carries the full transferred-in cost per unit, plus its share of the new conversion costs.

Example. Process 2 receives 3,000 units at a transfer cost of ₦30 each (₦90,000). During the month it adds conversion costs of ₦21,600. 2,400 units are completed and 600 remain in progress, 100% complete for transferred-in cost and 50% complete for conversion. There are no losses.

Finished goods = 2,400 × (₦30 + ₦8) = ₦91,200. Closing WIP = 600 × ₦30 + 300 × ₦8 = ₦18,000 + ₦2,400 = ₦20,400. Total ₦111,600 = ₦90,000 + ₦21,600. ✓ The completed units are then transferred to the next process, or to finished goods, at ₦38 each.

When the loss is found part-way through the process

So far, losses were assumed to be detected at the end of the process. If inspection takes place at an earlier stage, a lost unit has had only the cost incurred up to that point. For abnormal loss, count the equivalent units to the stage reached: full materials (if added at the start) but only the conversion cost done to that point.

Example. A process takes in 5,000 units, all materials added at the start. Normal loss is 400 units (no scrap value). Inspection happens when units are 60% complete for conversion. 4,500 units are completed and there is no closing WIP. Materials cost ₦46,000 and conversion costs ₦22,800.

• Physical units.
  5,000 − 400 normal loss − 4,500 completed = 100 units of abnormal loss.
• Equivalent units, materials.
  4,500 + 100 = 4,600.
  Conversion: 4,500 + (100 × 60% = 60) = 4,560.
  Normal loss units are not counted.
• Cost per equivalent unit.
  materials ₦46,000 ÷ 4,600 = ₦10.
  Conversion ₦22,800 ÷ 4,560 = ₦5.
• Finished goods.
  4,500 × ₦15 = ₦67,500.
  Abnormal loss = 100 × ₦10 + 60 × ₦5 = ₦1,000 + ₦300 = ₦1,300.
  Total ₦68,800 = ₦46,000 + ₦22,800. ✓

If the loss were assumed to occur at the end, abnormal loss would count 100 equivalent units of conversion, not 60, and the cost per unit of conversion would fall to ₦22,800 ÷ 4,600 = ₦4.96. The examiner will usually state when inspection occurs, so read the question for that detail.

Choosing between weighted average and FIFO

In the earlier worked comparison, FIFO valued finished goods at ₦45,860.57 and weighted average at ₦46,000, a difference of only ₦139. The two methods agree closely when costs change little from month to month. They differ more when prices move quickly, when opening WIP is a big part of the month’s activity or when the stage of completion of opening WIP is low.

The process account and the loss accounts

After the valuation, the figures are put into the process account, with quantities and values on both sides. The abnormal loss goes to an abnormal loss account (written off to the income statement net of any scrap value). Any scrap value of normal loss goes to a scrap account. For the earlier example with closing WIP and losses:

Check both columns: units 3,000 + 400 + 100 + 500 = 4,000 and values ₦24,000 + ₦400 + ₦800 + ₦3,600 = ₦28,800. If the columns do not balance, the cost per equivalent unit or a quantity is wrong.

Common mistakes in the exam

• Using one set of equivalent units for materials and conversion when completion differs.
• In weighted average, forgetting to add the cost of opening WIP to the current costs.
• In FIFO, including opening WIP costs in the cost per equivalent unit, or counting the opening units as fully worked this period.
• Counting normal loss units in the equivalent units.
• Leaving the abnormal loss out of equivalent units.
• Offsetting the scrap value of normal loss against conversion costs instead of materials.
• Not checking that the total valuation equals the total costs.
• Rounding cost per equivalent unit too early.

Quick revision

• Equivalent units = units × % complete. Separate figures for materials and conversion.
• Three stages: equivalent units; cost per equivalent unit; evaluation.
• Weighted average: pool opening WIP and current costs; equivalent units = finished + closing WIP.
• FIFO: current costs only; equivalent units = complete opening WIP + started and finished + closing WIP.
• Losses: normal loss excluded; abnormal loss included; scrap of normal loss offset against materials.
• Check: total value = opening WIP + costs of the period.

Practice questions

These are original questions written in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one before you open the answer.

Section A style: multiple choice

Section B style: written questions

A further written question

Model answers

Spotted a mistake? Tell us and we will check it.