We can use the formula for inventory turnover to determine the average inventory:

$\text{Turnover} = \frac{\text{Sales}}{\text{Average Inventory at Cost}}$

We are given:

• Sales = $100,000
• Turnover = 4
• Markup = 48%

Step 1: Determine Cost of Goods Sold (COGS)

Markup is based on cost, meaning:

$\text{Selling Price} = \text{Cost} + \text{Markup}$

$\text{Cost} = \frac{\text{Sales}}{1 + \text{Markup Percentage}}$

$\text{Cost} = \frac{100,000}{1.48} = 67,567.57$

Thus, COGS = $67,567.57.

Step 2: Calculate Average Inventory

Rearrange the inventory turnover formula:

$\text{Average Inventory at Cost} = \frac{\text{COGS}}{\text{Turnover}}$

$\text{Average Inventory} = \frac{67,567.57}{4} = 16,891.89$

Final Answer:

The average inventory is $16,891.89.

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Would you like a breakdown of why we used these formulas? Here are five related questions to deepen understanding:

1. How does inventory turnover affect business profitability?
2. What happens to average inventory if the turnover rate increases?
3. How does markup percentage affect the cost of goods sold?
4. Can a company increase sales while keeping the same inventory turnover?
5. Why is it important to distinguish between markup and margin?

Tip: A higher inventory turnover generally indicates efficient inventory management, but too high a turnover might mean stock shortages.