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What is the average inventory turnover for the firm?

Note: Round your answer to 3 decimal places.

To calculate the **average inventory turnover** for the firm, we use the formula:

\[
\text{Inventory Turnover} = \frac{\text{Cost of Goods Sold (COGS)}}{\text{Average Inventory}}
\]

### Step 1: Calculate Total Cost of Goods Sold (COGS)
From the image, the quarterly COGS values are:
- Quarter 1: 475 million USD
- Quarter 2: 508 million USD
- Quarter 3: 623 million USD
- Quarter 4: 700 million USD

\[
\text{Total COGS} = 475 + 508 + 623 + 700 = 2306 \, \text{million USD}
\]

### Step 2: Calculate Average Inventory
Average inventory is calculated by taking the sum of beginning and ending inventories for each quarter, divided by the number of periods. We'll consider **raw materials** and **work-in-process and finished goods** inventories at the Louisville plant, as well as **distribution center inventory** in the United States, Canada, and Europe.

For simplicity, we assume that the beginning inventory of Quarter 1 is the end-of-quarter inventory from the previous year, and the end-of-quarter inventory of Quarter 4 is used as such. 

#### Raw Materials Inventory
- Q1: 83 million USD
- Q2: 46 million USD
- Q3: 73 million USD
- Q4: 82 million USD

\[
\text{Average Raw Materials Inventory} = \frac{83 + 46 + 73 + 82}{4} = 71 \, \text{million USD}
\]

#### Work-in-Process and Finished Goods at Louisville
- Q1: 152 million USD
- Q2: 202 million USD
- Q3: 128 million USD
- Q4: 281 million USD

\[
\text{Average WIP & Finished Goods Inventory} = \frac{152 + 202 + 128 + 281}{4} = 190.75 \, \text{million USD}
\]

#### Distribution Center Inventory
For the distribution center inventories in the US, Canada, and Europe, sum them up:

- **Quarter 1 Total**: 29 (US) + 19 (Canada) + 6 (Europe) = 54 million USD
- **Quarter 2 Total**: 32 + 17 + 6 = 55 million USD
- **Quarter 3 Total**: 50 + 21 + 14 = 85 million USD
- **Quarter 4 Total**: 51 + 18 + 7 = 76 million USD

\[
\text{Average Distribution Center Inventory} = \frac{54 + 55 + 85 + 76}{4} = 67.5 \, \text{million USD}
\]

### Step 3: Calculate Total Average Inventory
Combine the average inventories:

\[
\text{Total Average Inventory} = 71 + 190.75 + 67.5 = 329.25 \, \text{million USD}
\]

### Step 4: Calculate Average Inventory Turnover
Using the formula:

\[
\text{Inventory Turnover} = \frac{2306}{329.25} \approx 7.004
\]

### Final Answer:
The average inventory turnover for the firm is **7.004** (rounded to three decimal places).

Would you like more details or have any questions? Here are 5 related questions you might be interested in:

1. How does the inventory turnover ratio affect the company's profitability?
2. What is the significance of a high or low inventory turnover ratio?
3. How can changes in sales or production impact inventory levels?
4. What strategies can be used to improve inventory turnover?
5. How does seasonal demand affect the calculation of average inventory?

**Tip**: A higher inventory turnover ratio typically indicates efficient management of inventory, leading to less capital tied up in unsold stock.

What is the average inventory turnover for the firm?

Explore how to calculate the average inventory turnover ratio for U.S. Airfilter with detailed financial data and step-by-step calculations. This example covers key financial ratios such as Cost of Goods Sold (COGS) and Average Inventory. Perfect for business or finance students.

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