## Equivalent Production — When Only Closing WIP is Given

Equivalent Production is a concept that converts partially completed units into equivalent fully completed units so that cost per unit can be calculated consistently.

### When is it Needed?

At the end of a period, some units are still in process (WIP). These units have absorbed some material, labour, and overhead — but not all. To compute a fair cost per unit, partially complete units must be expressed as their equivalent in fully complete units.

### Two Variants

1. Only Closing WIP is given (no opening WIP).

2. Both Opening and Closing WIP are given — solved using FIFO or Weighted Average method.

### Step-by-Step Approach (Only Closing WIP)

Step 1: Prepare the process account normally. The only difference will be in the valuation of:

Abnormal Loss
Abnormal Gain
Closing WIP

(They are now valued using equivalent units rather than physical units.)

Step 2: Prepare the Statement of Equivalent Production.

Step 3: Prepare the Statement of Cost to calculate cost per equivalent unit for each factor of production (Material, Labour, Overheads — separately).

Step 4: Apportion the cost to the various output categories on the basis of equivalent units.

### Format — Statement of Equivalent Production

	Units	Material %	Material Eq. Units	Labour %	Labour Eq. Units	OH %	OH Eq. Units
Normal Loss	100	—	—	—	—	—	—
Finished Goods	2,000	100%	2,000	100%	2,000	100%	2,000
Abnormal Loss	500	100%	500	50%	250	50%	250
Closing WIP	1,000	70%	700	50%	500	20%	200
Total			3,200		2,750		2,450

### Key Conventions

1. Normal Loss: Work done = 0% for all factors. (Normal loss is treated as if it never absorbed any input cost — its cost is borne by good units.)

2. Finished Goods: Work done = 100% on all factors.

3. Abnormal Loss: Usually assumed 100% complete for material, but partial completion (e.g., 50%) for labour and overheads depending on when in the process loss occurred.

4. Closing WIP: Has different % completion for each factor (material is usually added at the start, so often higher; labour and OH accrue gradually).

### Statement of Cost (Cost per Equivalent Unit)

```

Cost per Equivalent Unit (Material) = (Total Material Cost − Scrap Value of Normal Loss) / Equivalent Units of Material

Cost per Equivalent Unit (Labour) = Total Labour Cost / Equivalent Units of Labour

Cost per Equivalent Unit (Overheads) = Total OH / Equivalent Units of Overheads

```

### Apportionment

Multiply each cost-per-equivalent-unit by the equivalent units of FG, Abnormal Loss, and Closing WIP to get the value of each.

Worked example

### Example 1

Example (from notes): Input 3,600 units. Output: FG 2,000; Normal Loss 100; Abnormal Loss 500; Closing WIP 1,000.

Stage of completion:

FG — 100% on all
Abnormal Loss — 100% material, 50% labour & OH
Closing WIP — 70% material, 50% labour, 20% OH
Normal Loss — 0% on all

Equivalent Units:

Material = 2,000 + 0 + 500 + 700 = 3,200
Labour = 2,000 + 0 + 250 + 500 = 2,750
Overheads = 2,000 + 0 + 250 + 200 = 2,450

If Material cost = ₹64,000 (after normal loss scrap adjustment), then Cost per Eq. Unit (Material) = ₹64,000 / 3,200 = ₹20.

Closing WIP Material value = 700 × ₹20 = ₹14,000.

### Example 2

Abnormal Loss Valuation: If Material cost/eq unit = ₹20, Labour = ₹10, OH = ₹5, then:

Abnormal Loss value = (500 × ₹20) + (250 × ₹10) + (250 × ₹5) = ₹10,000 + ₹2,500 + ₹1,250 = ₹13,750

⚠️ Common exam mistakes

Assigning any equivalent units to Normal Loss — it must always be 0% across all factors.
Using the same % completion for all factors of production for Closing WIP — each factor has its own % completion.
Forgetting to deduct scrap value of normal loss from material cost before computing cost per equivalent unit.
Assuming Abnormal Loss is partially complete on material when the question implies it occurred after full material introduction (or vice versa).
Treating Finished Goods at less than 100% completion (FG is always 100% complete).
Mixing up physical units with equivalent units when preparing the Process A/c.

Reference:

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Equivalent Production — Statement of Equivalent Production (Closing WIP only)

Worked example

⚠️ Common exam mistakes