Given the transactions at Sara's Boutique for October, we need to calculate the ending inventory and the cost of goods sold (COGS) using the Last-In-First-Out (LIFO) method.
Let's go through the process step by step:
### 1. Calculate Total Units Purchased and Total Units Sold
#### Units Purchased:
- Beginning inventory (October 1): 6 units
- Purchase on October 10: 5 units
- Purchase on October 20: 4 units
- Purchase on October 30: 8 units
Adding these, the total units purchased:
[tex]\[ 6 + 5 + 4 + 8 = 23 \, \text{units} \][/tex]
#### Units Sold:
- Sale on October 4: 4 units
- Sale on October 13: 3 units
- Sale on October 28: 7 units
Adding these, the total units sold:
[tex]\[ 4 + 3 + 7 = 14 \, \text{units} \][/tex]
### 2. Calculate Ending Inventory
Starting inventory + Purchases - Sales = Ending inventory
[tex]\[ 6 + 17 - 14 = 9 \, \text{units} \][/tex]
### 3. Calculate Cost of Ending Inventory using LIFO
Using the LIFO method, we will take the cost of the most recent purchases first for the units that are left in the inventory.
- Last purchase (October 30): 8 units at [tex]$730/unit
- Second last purchase (October 20): 1 unit at $[/tex]720/unit
So the calculation for the ending inventory cost is as follows:
[tex]\[
8 \, \text{units} \times \$730 = \$5840 \][/tex]
[tex]\[ 1 \, \text{unit} \times \$720 = \$720
\][/tex]
Adding these together, we get:
[tex]\[ \$5840 + \$720 = \$6560 \][/tex]
### 4. Calculate Cost of Goods Sold (COGS) using LIFO
Using LIFO, we calculate COGS by subtracting the ending inventory cost from the total cost of available inventory:
Total cost of available goods:
- Beginning inventory: [tex]\(6 \, \text{units} \times \$700 = \$4200\)[/tex]
- Purchase on October 10: [tex]\(5 \, \text{units} \times \$710 = \$3550\)[/tex]
- Purchase on October 20: [tex]\(4 \, \text{units} \times \$720 = \$2880\)[/tex]
- Purchase on October 30: [tex]\(8 \, \text{units} \times \$730 = \$5840\)[/tex]
[tex]\[ \text{Total cost} = \$4200 + \$3550 + \$2880 + \$5840 = \$16470 \][/tex]
Ending Inventory Value (calculated from LIFO): [tex]\( \$6560 \)[/tex]
Thus, the Cost of Goods Sold (COGS) is:
[tex]\[ COGS = \text{Total cost} - \text{Ending Inventory Value} \][/tex]
[tex]\[ COGS = \$16470 - \$6560 = \$9910 \][/tex]
### Summarized Results:
- Ending Inventory (October 31): [tex]\( \$6560 \)[/tex]
- Cost of Goods Sold (October 31): [tex]\( \$9910 \)[/tex]
These results give us a clear picture of the cost assignment for inventory and sales for Sara's Boutique for the month of October using the LIFO method.
