Final answer:
Elaina should aim for an average inventory value of approximately $42,204.49 to reach her desired inventory turnover ratio of 4.9, based on her forecasted annual sales of $206,804.
Step-by-step explanation:
Elaina is looking to calcular her average aggregate inventory value based on a desired inventory turnover ratio of 4.9. The inventory turnover ratio is calculated by dividing the cost of goods sold (COGS) by the average inventory value over a certain time period. Since Elaina has forecasted her weekly sales to be $3,977, and plans to operate 52 weeks a year, her annual sales are forecasted to be $3,977 * 52 = $206,804. To achieve her targeted turnover ratio, we use the formula:
Inventory Turnover Ratio = Annual Sales / Average Inventory Value
Thus, Average Inventory Value = Annual Sales / Inventory Turnover Ratio = $206,804 / 4.9 ≈ $42,204.49. Elaina should aim for her average inventory value to be approximately $42,204.49 to achieve the inventory turnover ratio of 4.9.