Math Problem Statement

Assuming average cost, what is the ending inventory after the July 14 sale? (Round any intermediary calculations to the nearest cent and your final answer to the nearest dollar.)

Solution

To solve this inventory problem using the average cost method, let's go through each transaction and calculate the weighted average cost per unit after each inventory update. Then, we'll calculate the ending inventory after the final sale on July 14.

Inventory Data Summary:

  1. July 1 - Beginning Inventory: 5 units at $48 each.
  2. July 4 - Purchase: 10 units at $54 each.
  3. July 7 - Sale: 12 units.
  4. July 11 - Purchase: 9 units at $60 each.
  5. July 14 - Sale: 8 units.

Steps:

Step 1: Calculate Average Cost after July 4 Purchase

  • Total Units after purchase on July 4 = 5 (beginning) + 10 (purchase) = 15 units.
  • Total Cost = (5 × $48) + (10 × $54) = $240 + $540 = $780.
  • Average Cost per Unit = $780 ÷ 15 ≈ $52.00.

Step 2: Update Inventory after July 7 Sale

  • Units Sold = 12 units.
  • Remaining Units = 15 - 12 = 3 units.
  • Cost of Remaining Units = 3 × $52.00 = $156.

Step 3: Calculate Average Cost after July 11 Purchase

  • Total Units after purchase on July 11 = 3 (remaining) + 9 (purchase) = 12 units.
  • Total Cost = $156 (remaining) + (9 × $60) = $156 + $540 = $696.
  • Average Cost per Unit = $696 ÷ 12 = $58.00.

Step 4: Update Inventory after July 14 Sale

  • Units Sold = 8 units.
  • Remaining Units = 12 - 8 = 4 units.
  • Cost of Remaining Units = 4 × $58.00 = $232.

Final Answer

The ending inventory after the July 14 sale is $232.

Thus, the correct answer is: B. $232

Would you like any further details on the steps involved? Here are some related questions:

  1. What would be the ending inventory if a different inventory costing method was used, such as FIFO?
  2. How does the average cost method affect financial reporting compared to LIFO or FIFO?
  3. What is the impact of frequent price changes on the average cost method?
  4. How would inventory valuation change if more purchases were made before the final sale?
  5. Can the average cost method be combined with other costing methods in real-world scenarios?

Tip: Average cost per unit recalculations should be done after every purchase when using the average cost method.

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Math Problem Analysis

Mathematical Concepts

Inventory Valuation
Average Cost Method

Formulas

Average Cost per Unit = Total Cost / Total Units
Ending Inventory Value = Remaining Units × Average Cost per Unit

Theorems

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Suitable Grade Level

Grades 11-12