Equivalent Units of Production: Weighted average method

The following information concerns production in the Finishing Department for May. The Finishing Department uses the Weighted average method.

ACCOUNT Work in Process—Finishing Department              ACCOUNT NO.
Date	Item	Debit	Credit	Balance
Debit	Balance
Credit
May 1	Bal., 17,200 units, 75% completed	 	 	103,200
31	Direct materials, 84,300 units	308,538	 	411,738
31	Direct labor	191,300	 	603,038
31	Factory overhead	194,400	 	797,438
31	Goods transferred, 89,400 units	 	767,052	30,386
31	Bal., ? units, 35% completed	 	 	30,386
a.  Determine the number of units in work in process inventory at the end of the month.
fill in the blank 1 of 1
12,100
units

b.  Determine the number of whole units to be accounted for and to be assigned costs and the equivalent units of production for May. Assume that direct materials are placed in process during production.

Line Item Description	Units
Whole units to be accounted for	fill in the blank 1 of 3
101,500
units
Whole units to be assigned costs	fill in the blank 2 of 3
101,500
units
Equivalent units of production	fill in the blank 3 of 3
units
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a. Assume that the items in beginning inventory were the first items completed during the period. How many then were started and completed during the period? How many units were started during the period but are still in process at the end of the period?

b. How many units were started during the current period? How many units were complete at the end of the period? How many units were still in work in process? How much in resources had these units in ending work in process consumed during the current period?

To solve this problem using the weighted average method, we need to calculate several key figures:

### Part A: Number of Units in Work in Process (WIP) at the End of the Month

Given that 89,400 units were transferred out, and there were 17,200 units in the beginning WIP, we can calculate the ending WIP as follows:

- **Total units to account for:**
  \[
  \text{Units in beginning WIP} + \text{Units started} = \text{Units transferred out} + \text{Ending WIP units}
  \]
  \[
  17,200 + 84,300 = 89,400 + \text{Ending WIP units}
  \]
  \[
  101,500 = 89,400 + \text{Ending WIP units}
  \]
  \[
  \text{Ending WIP units} = 101,500 - 89,400 = 12,100 \text{ units}
  \]
This confirms the ending WIP is 12,100 units.

### Part B: Units to be Accounted for, Assigned Costs, and Equivalent Units of Production

1. **Whole Units to be Accounted for:**

   This includes units in the beginning WIP and the units started during May:
   \[
   \text{Whole units to be accounted for} = 17,200 (\text{Beginning WIP}) + 84,300 (\text{Started}) = 101,500 \text{ units}
   \]

2. **Whole Units to be Assigned Costs:**

   Since the weighted average method considers the total units (beginning + started), the whole units to be assigned costs will also be:
   \[
   101,500 \text{ units}
   \]

3. **Equivalent Units of Production (EUP):**

   The equivalent units of production consider the completion percentages:

   - **Units completed and transferred out:** 89,400 units (since they are fully completed, they contribute fully to the EUP)
   - **Ending WIP units:** 12,100 units at 35% completion contribute to EUP
   - For direct materials, which are usually added at the start, 12,100 units contribute fully.

   Therefore:
   \[
   \text{EUP for materials} = 89,400 + 12,100 \times 100\% = 101,500 \text{ units}
   \]
   \[
   \text{EUP for conversion costs} = 89,400 + 12,100 \times 35\% = 89,400 + 4,235 = 93,635 \text{ units}
   \]

### Answers:
1. **Whole units to be accounted for:** 101,500 units
2. **Whole units to be assigned costs:** 101,500 units
3. **Equivalent units of production:** 93,635 units for conversion costs

### Additional Questions:
1. How do the equivalent units of production differ for materials versus conversion costs?
2. What would change if the beginning WIP was at a different completion percentage?
3. How does the weighted average method affect cost per unit compared to FIFO?
4. If direct materials were added at the end of production, how would this affect the EUP?
5. How would a higher completion percentage of ending WIP affect the equivalent units of production?

**Tip:** Always remember to carefully distinguish between materials and conversion costs when calculating equivalent units of production.

Learn how to calculate equivalent units of production using the weighted average method in cost accounting. This detailed solution covers determining units in work in process, whole units to be accounted for and assigned costs, and calculating equivalent units for materials and conversion costs.

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