Alright, let's work through this problem step-by-step to determine the weighted-average cost per unit for Crane Company's inventory.
1. Determine Total Units and Total Cost by Aggregating Inventory and Purchases:
- Start with the initial inventory and add the purchases throughout the year.
- Using the given data:
- January inventory: 10,000 units at \[tex]$10.00 each.
- June purchases: 5,000 units at \$[/tex]8.00 each.
- November purchases: 5,000 units at \[tex]$8.00 each.
2. Calculate the Total Number of Units:
\[
\text{Total units} = \text{January inventory units} + \text{June purchases units} + \text{November purchases units}
\]
\[
\text{Total units} = 10,000 + 5,000 + 5,000 = 20,000 \text{ units}
\]
3. Calculate the Total Cost:
\[
\text{Total cost} = (\text{January inventory units} \times \text{January inventory cost}) + (\text{June purchases units} \times \text{June purchases cost}) + (\text{November purchases units} \times \text{November purchases cost})
\]
\[
\text{Total cost} = (10,000 \times 10.00) + (5,000 \times 8.00) + (5,000 \times 8.00)
\]
\[
\text{Total cost} = 100,000 + 40,000 + 40,000 = 180,000 \text{ dollars}
\]
4. Calculate the Weighted-Average Cost per Unit:
\[
\text{Weighted average cost per unit} = \frac{\text{Total cost}}{\text{Total units}}
\]
\[
\text{Weighted average cost per unit} = \frac{180,000}{20,000} = 9.00 \text{ dollars}
\]
5. Select the Correct Weighted-Average Cost per Unit:
- The choices given are \$[/tex]9.00, \[tex]$8.70, and \$[/tex]8.85.
- Based on our calculations, the weighted-average cost per unit is \[tex]$9.00.
Thus, the correct weighted-average cost per unit is \$[/tex]9.00.
