Sure! Let's determine the cost of ending inventory using different inventory valuation methods: FIFO (First-In, First-Out), LIFO (Last-In, First-Out), and the weighted-average method.
### Given data:
[tex]\[
\begin{array}{llrrr}
\text{Beginning Inventory and Purchases} & & \text{Boxes} & \text{Box Cost} & \text{Total Cost} \\
\hline
\text{Beginning Inventory: January 1} & & 14,800 & \$8 & \$118,400 \\
\text{March 1} & & 5,800 & \$9 & \$52,200 \\
\text{June 1} & & 1,800 & \$13 & \$23,400 \\
\text{September 1} & & 1,150 & \$16 & \$18,400 \\
\text{December 1} & & 1,100 & \$25 & \$22,500 \\
\hline
\text{Total} & & 24,650 & & \$235,900 \\
\hline \hline
\end{array}
\][/tex]
Now, we need to find the cost of ending inventory for 550 obsolete boxes using each method.
### FIFO (First-In, First-Out) Method:
According to the FIFO method, the oldest inventory costs are assigned first. Therefore, we consider the costs from January 1 first, then continue in chronological order until we count the 550 obsolete boxes.
- Start with the boxes from January 1:
[tex]\[
\text{Boxes used from January 1} = 550 \quad \text{at }\$8 \text{ per box}
\][/tex]
[tex]\[
\text{FIFO Inventory Cost} = 550 \times 8 = \$4,400
\][/tex]
### LIFO (Last-In, First-Out) Method:
According to the LIFO method, the most recent inventory costs are assigned first. Therefore, we consider the costs from December 1 first, then go backward chronologically.
- Start with the boxes from December 1:
[tex]\[
\text{Boxes used from December 1} = 1,100 \quad \text{at }\$25 \text{ per box}
\][/tex]
Since the boxes required are 550 (which is less than 1,100), the cost will be:
[tex]\[
\text{LIFO Inventory Cost} = 550 \times 25 = \$13,750
\][/tex]
### Weighted-Average Method:
The weighted-average cost per unit is calculated by dividing the total cost by the total number of units. Multiply this average cost by the number of obsolete boxes.
- Calculate the total cost and total number of boxes:
[tex]\[
\text{Total Cost} = \$235,900
\][/tex]
[tex]\[
\text{Total Boxes} = 24,650
\][/tex]
[tex]\[
\text{Weighted-Average Cost per Unit} = \frac{\text{Total Cost}}{\text{Total Boxes}} = \frac{235,900}{24,650} = \$9.57 \, \text{(rounded to 2 decimal places)}
\][/tex]
- Calculate the cost for 550 boxes using weighted-average cost:
[tex]\[
\text{Weighted-Average Inventory Cost} = 550 \times 9.57 = \$5,263.50 \, \text{(rounded to 2 decimal places)}
\][/tex]
Since the final answers are rounded to the nearest dollar:
- Weighted-Average Inventory Cost = \[tex]$5,353
### Summary:
\[
\begin{array}{|l|l|}
\hline
\text{Method} & \text{Ending Inventory Cost} \\
\hline
\text{FIFO} & \$[/tex]4,400 \\
\text{LIFO} & \[tex]$13,750 \\
\text{Weighted-average} & \$[/tex]5,353 \\
\hline
\end{array}
\]
Therefore, the costs of the ending inventory using FIFO, LIFO, and the weighted-average method are \[tex]$4,400, \$[/tex]13,750, and \$5,353 respectively.
