Certainly! Let's calculate the cost of ending inventory and cost of goods sold (COGS) using the FIFO, LIFO, and Average-Cost methods step by step.
### Given Data
- Beginning Inventory: 110 units at [tex]$5 per unit
- Purchase on June 12: 350 units at $[/tex]6 per unit
- Purchase on June 23: 190 units at [tex]$7 per unit
- Ending Inventory: 193 units
### 1. Calculating FIFO (First-In, First-Out)
Under FIFO, the first units purchased are the first ones sold. Therefore, the ending inventory consists of the most recently purchased units.
#### Cost of Ending Inventory (FIFO)
1. June 23 purchase:
- Ending inventory units: 193
- Units from June 23: 190 units at $[/tex]7 each
- Total cost from June 23: [tex]\(190 \times 7 = \$1,330\)[/tex]
2. Remaining units:
- Remaining units after June 23: [tex]\(193 - 190 = 3\)[/tex] units
- Units from June 12: 3 units at [tex]$6 each
- Total cost from June 12: \(3 \times 6 = \$[/tex]18\)
3. Total cost of ending inventory (FIFO):
- [tex]\( \$1,330 + \$18 = \$1,348 \)[/tex]
#### Cost of Goods Sold (FIFO)
1. Total available units for sale:
- Beginning Inventory: 110 units
- June 12 purchase: 350 units
- June 23 purchase: 190 units
- Total: [tex]\( 110 + 350 + 190 = 650 \)[/tex] units
2. Units sold:
- [tex]\( 650 - 193 = 457 \)[/tex] units
3. Cost of units sold under FIFO:
- Beginning Inventory: 110 units at [tex]$5 = \$[/tex]550
- June 12 purchase: 350 units at [tex]$6 = \$[/tex]2,100
- Remaining units from June 23: [tex]\( 457 - 460 = 3 \times 7 = \$21 \)[/tex]
- Total cost of goods sold (FIFO): [tex]\( 550 + 2,100 + 21 = \$2,632 \)[/tex]
### 2. Calculating LIFO (Last-In, First-Out)
Under LIFO, the last units purchased are the first ones sold. Therefore, the ending inventory consists of the earliest purchased units.
#### Cost of Ending Inventory (LIFO)
1. Beginning inventory:
- 110 units at [tex]$5 each
- Total cost from beginning inventory: \( 110 \times 5 = \$[/tex]550 \)
2. Remaining units:
- Remaining units after the beginning inventory: [tex]\( 193 - 110 = 83 \units \)[/tex]
- Units from June 12: 83 units at [tex]$6 each
- Total cost from June 12: \( 83 \times 6 = \$[/tex]498 \)
3. Total cost of ending inventory (LIFO):
- [tex]\( \$550 + \$498= \$1,048 \)[/tex]
#### Cost of Goods Sold (LIFO)
1. Cost of units sold under LIFO:
- June 23 purchase: 190 units at [tex]$7 = \$[/tex]1,330
- June 12 purchase: 350 units at [tex]$6 = \$[/tex]2,100
- Remaining cost from Beginning Inventory: [tex]\( 457 - 540 = 53 \times 5 = \$265 \)[/tex]
- Total cost of goods sold (LIFO): [tex]\( 1,330 + 2,100 + 265 = \$2,932 \)[/tex]
### 3. Calculating Average-Cost
The average-cost method uses the weighted average of all units available for sale during the period.
#### Average Cost per Unit:
1. Total cost:
- Beginning Inventory: 110 units at [tex]$5 = \$[/tex]550
- June 12 purchase: 350 units at [tex]$6 = \$[/tex]2,100
- June 23 purchase: 190 units at [tex]$7 = \$[/tex]1,330
- Total cost: [tex]\( \$550 + \$2,100 + \$1,330 = \$3,980 \)[/tex]
2. Total units:
- 110 + 350 + 190 = 650 units
3. Average cost per unit:
- [tex]\( \$3,980 / 650 \approx \$6.123 \)[/tex]
#### Cost of Ending Inventory (Average-Cost)
1. Ending inventory units: 193 units
2. Total cost: [tex]\( 193 \times \$6.123 \approx \$1,182 \)[/tex]
#### Cost of Goods Sold (Average-Cost)
1. Units sold: 457 units
2. Total cost: [tex]\( 457 \times \$6.123 \approx \$2,798 \)[/tex]
### Summary:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline & FIFO & LIFO & Average-Cost \\
\hline \text{Cost of the ending inventory} & \$1,348 & \$1,048 & \$1,182 \\
\hline \text{Cost of goods sold} & \$2,632 & \$2,932 & \$2,798 \\
\hline
\end{tabular}
\][/tex]
Therefore, the cost of ending inventory and the cost of goods sold under each method are:
1. FIFO:
- Ending Inventory: \[tex]$1,348
- Cost of Goods Sold: \$[/tex]2,632
2. LIFO:
- Ending Inventory: \[tex]$1,048
- Cost of Goods Sold: \$[/tex]2,932
3. Average-Cost:
- Ending Inventory: \[tex]$1,182
- Cost of Goods Sold: \$[/tex]2,798
