Step 1: Understand the periodic inventory system. Under this system, inventory is updated at the end of the accounting period, and the cost of goods sold (COGS) is calculated based on the changes in inventory and purchases during the period.
Step 2: Recall the formula for COGS under the periodic inventory system. The correct formula is: \( \text{COGS} = \text{Beginning Inventory} + \text{Purchases} - \text{Ending Inventory} \). This formula accounts for the inventory available for sale during the period and subtracts the ending inventory to determine the goods sold.
Step 3: Analyze the components of the formula: \( \text{Beginning Inventory} \) represents the inventory at the start of the period, \( \text{Purchases} \) are the goods bought during the period, and \( \text{Ending Inventory} \) is the inventory remaining at the end of the period.
Step 4: Compare the given options to the correct formula. The correct option matches \( \text{COGS} = \text{Beginning Inventory} + \text{Purchases} - \text{Ending Inventory} \). Other options do not align with the logic of the periodic inventory system.
Step 5: Apply this formula in practice by substituting the values for beginning inventory, purchases, and ending inventory to compute the cost of goods sold for a given period.