- The objective is to minimize the Cost of Goods Sold (COGS) to maximize gross profit, given constant sales revenue.
- Calculating COGS for each method: FIFO results in \(\$3510.00\), Average-Cost results in \(\$3712.50\), and LIFO results in \(\$3915.00\).
- Since FIFO yields the lowest COGS among the three methods, it results in the highest gross profit.
- Therefore, the FIFO method is the correct inventory valuation method to maximize gross profit. \(\boxed{\text{the FIFO method.}}\)
Explanation
- Analysis of Data and Objectives
To determine which inventory method results in the highest gross profit, we first identify the objective: maximizing gross profit, which is equivalent to minimizing the Cost of Goods Sold (COGS) since sales revenue remains constant across all methods.
We are given the following inventory purchases:
- June 1: 135 units at a cost of \(\$810\), which is \(\$810 / 135 = \$6\) per unit.
- June 10: 180 units at a cost of \(\$1440\), which is \(\$1440 / 180 = \$8\) per unit.
- June 15: 180 units at a cost of \(\$1260\), which is \(\$1260 / 180 = \$7\) per unit.
- June 28: 135 units at a cost of \(\$1215\), which is \(\$1215 / 135 = \$9\) per unit.
The total units available are \(135 + 180 + 180 + 135 = 630\) units, and the total cost is \(\$810 + \$1440 + \$1260 + \$1215 = \$4725\). A physical count on June 30 shows \(135\) units remaining, meaning \(630 - 135 = 495\) units were sold.
- Calculating COGS under FIFO, LIFO, and Average-Cost Methods
Now we calculate the COGS under each of the three standard methods:
- FIFO (First-In, First-Out): Under FIFO, the oldest units are sold first, so the ending inventory consists of the most recently purchased units. The 135 units remaining correspond to the purchase on June 28 at \(\$9\) per unit.
- Ending Inventory = \(135 \text{ units} \times \$9 = \$1215\).
- COGS = \(\text{Total Cost} - \text{Ending Inventory} = \$4725 - \$1215 = \$3510\).
- LIFO (Last-In, First-Out): Under LIFO, the most recent units are sold first, so the ending inventory consists of the oldest units. The 135 units remaining correspond to the purchase on June 1 at \(\$6\) per unit.
- Ending Inventory = \(135 \text{ units} \times \$6 = \$810\).
- COGS = \(\text{Total Cost} - \text{Ending Inventory} = \$4725 - \$810 = \$3915\).
- Average-Cost: We calculate the weighted-average cost per unit.
- Average Unit Cost = \(\text{Total Cost} / \text{Total Units} = \$4725 / 630 = \$7.50\) per unit.
- Ending Inventory = \(135 \text{ units} \times \$7.50 = \$1012.50\).
- COGS = \(\text{Total Cost} - \text{Ending Inventory} = \$4725 - \$1012.50 = \$3712.50\).
- Comparison and Conclusion
Comparing the calculated COGS for each method:
- FIFO: \(\$3510.00\)
- Average-Cost: \(\$3712.50\)
- LIFO: \(\$3915.00\)
The FIFO method results in the lowest Cost of Goods Sold (\(\$3510.00\)). Since maximizing gross profit is achieved by minimizing COGS, the FIFO method results in the highest gross profit. Therefore, the correct choice is the FIFO method.
Examples
Inventory management is crucial for retail businesses to maintain profitability. For instance, a grocery store selling perishable items naturally uses a FIFO approach to ensure that the oldest stock is sold before it expires. By understanding how different inventory valuation methods impact the financial reports, managers can make informed decisions to optimize their tax liabilities and report the most accurate gross profit for their operations.