To calculate the ending inventory and cost of goods sold (COGS) using the weighted-average cost method in a periodic inventory system, follow these steps:

Step 1: Calculate the Weighted-Average Cost per Unit

The weighted average cost is calculated as the total cost of all units available for sale divided by the total number of units available for sale.

We need to consider both the beginning inventory and the purchases made throughout the month.

Units Available for Sale:

• Beginning inventory: 6 units
• Purchases on October 10: 5 units
• Purchases on October 20: 4 units
• Purchases on October 30: 6 units

Total Units Available for Sale = 6 + 5 + 4 + 6 = 21 units

Total Cost of Goods Available for Sale:

• Beginning inventory: $6 \times 720 = 4,320$
• Purchases on October 10: $5 \times 730 = 3,650$
• Purchases on October 20: $4 \times 740 = 2,960$
• Purchases on October 30: $6 \times 750 = 4,500$

Total Cost = 4,320 + 3,650 + 2,960 + 4,500 = 15,430

Weighted-Average Cost per Unit = Total Cost / Total Units $\text{Weighted-Average Cost per Unit} = \frac{15,430}{21} = 734.2857$ (Rounded to 4 decimal places)

Step 2: Calculate the Cost of Goods Sold (COGS)

Now, let's calculate the COGS by using the weighted-average cost per unit and the number of units sold during the month.

Total Units Sold:

• Sale on October 4: 4 units
• Sale on October 13: 3 units
• Sale on October 28: 7 units

Total Units Sold = 4 + 3 + 7 = 14 units

COGS = Weighted-Average Cost per Unit × Units Sold $\text{COGS} = 734.2857 \times 14 = 10,260.00$ (Rounded to 2 decimal places)

Step 3: Calculate the Ending Inventory

Finally, calculate the ending inventory, which is the cost of the unsold units. We have 21 units available for sale, and 14 units were sold, so the number of units remaining in inventory is:

Ending Inventory Units = 21 - 14 = 7 units

Ending Inventory = Weighted-Average Cost per Unit × Ending Inventory Units $\text{Ending Inventory} = 734.2857 \times 7 = 5,140.00$ (Rounded to 2 decimal places)

Final Answers:

• Cost of Goods Sold (COGS): $10,260.00
• Ending Inventory: $5,140.00

Would you like further details on the weighted-average method or help with any other related questions?

Related Questions:

1. What is the difference between the periodic and perpetual inventory systems?
2. How does the FIFO method differ from the weighted-average method in inventory calculation?
3. How do you calculate inventory turnover ratio and what does it indicate?
4. If Alexandra's Boutique used FIFO instead of weighted-average, how would that affect the ending inventory and COGS?
5. What is the impact of the inventory valuation method on the financial statements (Income Statement and Balance Sheet)?

Tip: Always double-check your rounding when working with weighted averages to ensure you don’t lose precision!