Answer :
To solve this problem of calculating the cost of goods available for sale, ending inventory, and cost of goods sold for Aircard Corporation using different inventory costing methods (FIFO, LIFO, and Weighted Average Cost), we need to carefully follow each step of the process. Let's break down the solution step-by-step according to the data provided for the month of July.
### Step 1: Understand the Transactions and Costs
We start with the transactions and costs information provided:
1. Beginning Inventory:
- Units: 2,000
- Unit Cost: \[tex]$40 2. Purchases: - July 13: 6,000 units at \$[/tex]44 per unit
- July 25: 8,000 units at \[tex]$50 per unit 3. Sales: - July 5: 1,000 units - July 17: 3,900 units - July 27: 5,000 units ### Step 2: Calculate Total Units and Cost Available for Sale - Beginning Inventory: - Total cost: 2,000 units * \$[/tex]40/unit = \[tex]$80,000 - First Purchase: - Total cost: 6,000 units * \$[/tex]44/unit = \[tex]$264,000 - Second Purchase: - Total cost: 8,000 units * \$[/tex]50/unit = \[tex]$400,000 Total Cost of Goods Available for Sale: \[ 80,000 + 264,000 + 400,000 = \$[/tex]744,000 \]
Total Units Available for Sale:
[tex]\[ 2,000 + 6,000 + 8,000 = 16,000 \text{ units} \][/tex]
### Step 3: Calculate Total Units Sold
Total Units Sold:
[tex]\[ 1,000 \text{ units } + 3,900 \text{ units } + 5,000 \text{ units } = 9,900 \text{ units } \][/tex]
### Step 4: Calculate Ending Inventory Units
Ending Inventory Units:
[tex]\[ 16,000 \text{ units } - 9,900 \text{ units } = 6,100 \text{ units } \][/tex]
### Calculations for Different Methods
#### (a) FIFO Method
FIFO assumes that the oldest inventory items are sold first.
1. Entire beginning inventory (2,000 units at \[tex]$40 each) is sold first. 2. Next, we sell from the first purchase (6,000 units at \$[/tex]44 each).
3. Our ending inventory will come from the most recent purchase (price at end).
- Cost of Goods Sold:
[tex]\[ (2000 \text{ units} \times \$40) + (6,000 \text{ units} \times \$44) + (1,900 \text{ units} \times \$50) = \$80,000 + \$264,000 + \$95,000 = \$439,000 \][/tex]
- Ending Inventory:
[tex]\[ (3,800 \text{ units} \times \$50) = \$190,000 \][/tex]
#### (b) LIFO Method
LIFO assumes that the most recently-purchased items are sold first.
1. Sell from the most recent purchase first (8,000 at \[tex]$50). 2. Remaining units are sold from the earlier batches. - Cost of Goods Sold: \[ (8,000 \text{ units} \times \$[/tex]50) + (1,900 \text{ units} \times \[tex]$44) = \$[/tex]400,000 + \[tex]$83,600 = \$[/tex]483,600
\]
- Ending Inventory:
[tex]\[ (2,000 \text{ units} \times \$40) + (4,100 \text{ units} \times \$44) = \$80,000 + \$180,400 = \$260,400 \][/tex]
#### (c) Weighted Average Method
The weighted average unit cost is calculated based on the total cost and total units.
1. Weighted average cost per unit:
[tex]\[ \text{Average Unit Cost} = \frac{\text{Total Cost}}{\text{Total Units}} = \frac{\$744,000}{16,000} = \$46.50 \text{ per unit} \][/tex]
- Ending Inventory:
[tex]\[ \text{Ending Inventory Cost} = 6,100 \text{ units} \times \$46.50 \text{ per unit} = \$283,650 \][/tex]
- Cost of Goods Sold:
[tex]\[ \text{Total Cost of Goods Sold} = \$744,000 - \$283,650 = \$460,350 \][/tex]
### Summarized Results
| | FIFO | LIFO | Weighted Average |
|-----------------------|----------------|----------------|--------------------|
| Cost of Goods Available for Sale | \[tex]$744,000 | \$[/tex]744,000 | \[tex]$744,000 | | Ending Inventory | \$[/tex]190,000 | \[tex]$260,400 | \$[/tex]283,650 |
| Cost of Goods Sold | \[tex]$554,000 | \$[/tex]483,600 | \$460,350 |
### Conclusion
By following each step methodically, we obtained the costs for goods sold and the valuation of the ending inventory under three different costing methods: FIFO, LIFO, and Weighted Average. This analysis helps Aircard Corporation understand the financial impacts of their chosen inventory costing method.
### Step 1: Understand the Transactions and Costs
We start with the transactions and costs information provided:
1. Beginning Inventory:
- Units: 2,000
- Unit Cost: \[tex]$40 2. Purchases: - July 13: 6,000 units at \$[/tex]44 per unit
- July 25: 8,000 units at \[tex]$50 per unit 3. Sales: - July 5: 1,000 units - July 17: 3,900 units - July 27: 5,000 units ### Step 2: Calculate Total Units and Cost Available for Sale - Beginning Inventory: - Total cost: 2,000 units * \$[/tex]40/unit = \[tex]$80,000 - First Purchase: - Total cost: 6,000 units * \$[/tex]44/unit = \[tex]$264,000 - Second Purchase: - Total cost: 8,000 units * \$[/tex]50/unit = \[tex]$400,000 Total Cost of Goods Available for Sale: \[ 80,000 + 264,000 + 400,000 = \$[/tex]744,000 \]
Total Units Available for Sale:
[tex]\[ 2,000 + 6,000 + 8,000 = 16,000 \text{ units} \][/tex]
### Step 3: Calculate Total Units Sold
Total Units Sold:
[tex]\[ 1,000 \text{ units } + 3,900 \text{ units } + 5,000 \text{ units } = 9,900 \text{ units } \][/tex]
### Step 4: Calculate Ending Inventory Units
Ending Inventory Units:
[tex]\[ 16,000 \text{ units } - 9,900 \text{ units } = 6,100 \text{ units } \][/tex]
### Calculations for Different Methods
#### (a) FIFO Method
FIFO assumes that the oldest inventory items are sold first.
1. Entire beginning inventory (2,000 units at \[tex]$40 each) is sold first. 2. Next, we sell from the first purchase (6,000 units at \$[/tex]44 each).
3. Our ending inventory will come from the most recent purchase (price at end).
- Cost of Goods Sold:
[tex]\[ (2000 \text{ units} \times \$40) + (6,000 \text{ units} \times \$44) + (1,900 \text{ units} \times \$50) = \$80,000 + \$264,000 + \$95,000 = \$439,000 \][/tex]
- Ending Inventory:
[tex]\[ (3,800 \text{ units} \times \$50) = \$190,000 \][/tex]
#### (b) LIFO Method
LIFO assumes that the most recently-purchased items are sold first.
1. Sell from the most recent purchase first (8,000 at \[tex]$50). 2. Remaining units are sold from the earlier batches. - Cost of Goods Sold: \[ (8,000 \text{ units} \times \$[/tex]50) + (1,900 \text{ units} \times \[tex]$44) = \$[/tex]400,000 + \[tex]$83,600 = \$[/tex]483,600
\]
- Ending Inventory:
[tex]\[ (2,000 \text{ units} \times \$40) + (4,100 \text{ units} \times \$44) = \$80,000 + \$180,400 = \$260,400 \][/tex]
#### (c) Weighted Average Method
The weighted average unit cost is calculated based on the total cost and total units.
1. Weighted average cost per unit:
[tex]\[ \text{Average Unit Cost} = \frac{\text{Total Cost}}{\text{Total Units}} = \frac{\$744,000}{16,000} = \$46.50 \text{ per unit} \][/tex]
- Ending Inventory:
[tex]\[ \text{Ending Inventory Cost} = 6,100 \text{ units} \times \$46.50 \text{ per unit} = \$283,650 \][/tex]
- Cost of Goods Sold:
[tex]\[ \text{Total Cost of Goods Sold} = \$744,000 - \$283,650 = \$460,350 \][/tex]
### Summarized Results
| | FIFO | LIFO | Weighted Average |
|-----------------------|----------------|----------------|--------------------|
| Cost of Goods Available for Sale | \[tex]$744,000 | \$[/tex]744,000 | \[tex]$744,000 | | Ending Inventory | \$[/tex]190,000 | \[tex]$260,400 | \$[/tex]283,650 |
| Cost of Goods Sold | \[tex]$554,000 | \$[/tex]483,600 | \$460,350 |
### Conclusion
By following each step methodically, we obtained the costs for goods sold and the valuation of the ending inventory under three different costing methods: FIFO, LIFO, and Weighted Average. This analysis helps Aircard Corporation understand the financial impacts of their chosen inventory costing method.
