To calculate the requested values, we follow these steps:

Step 1: Calculate the Average Inventory

The formula for Average Inventory is: $\text{Average Inventory} = \frac{\text{Beginning Inventory} + \text{Ending Inventory}}{2}$ Given:

• Beginning Inventory = $75,200
• Ending Inventory = $105,225

$\text{Average Inventory} = \frac{75,200 + 105,225}{2} = \frac{180,425}{2} = 90,213 \, (\text{rounded to the nearest dollar})$

Step 2: Calculate the Inventory Turnover

The formula for Inventory Turnover is: $\text{Inventory Turnover} = \frac{\text{Cost of Goods Sold}}{\text{Average Inventory}}$ Given:

• Cost of Goods Sold = $135,250
• Average Inventory = $90,213

$\text{Inventory Turnover} = \frac{135,250}{90,213} \approx 1.5 \, (\text{rounded to the nearest tenth})$

Step 3: Compare with the Published Rate

The published rate is 4.8. The calculated Inventory Turnover (1.5) is less than the published rate, so we need to calculate the Target Average Inventory to match the published rate.

Step 4: Calculate the Target Average Inventory

The formula to find the Target Average Inventory is: $\text{Target Average Inventory} = \frac{\text{Cost of Goods Sold}}{\text{Published Rate}}$ Given:

• Cost of Goods Sold = $135,250
• Published Rate = 4.8

$\text{Target Average Inventory} = \frac{135,250}{4.8} = 28,177 \, (\text{rounded to the nearest dollar})$

Final Answers

• Average Inventory: $90,213
• Inventory Turnover: 1.5
• Target Average Inventory: $28,177

Observations

Since the actual turnover (1.5) is less than the published rate (4.8), the target average inventory is $28,177 to achieve the industry standard.

Let me know if you need clarification or further steps! Here are 5 related questions and a tip:

1. What does a higher inventory turnover rate indicate about a company's operations?
2. How can companies improve their inventory turnover ratio?
3. What is the impact of high inventory levels on a company’s finances?
4. Why is it important to match or exceed the industry standard turnover rate?
5. How do seasonal businesses calculate turnover ratios effectively?

Tip: Always review your inventory levels and sales cycles regularly to adjust to market trends and maintain optimal turnover rates.