Problem 13 - Accounting Principles

Question

Carlos Company had beginning inventory of \(\$ 80,000\), end- (SO 5) ing inventory of \(\$ 110,000\), cost of goods sold of \(\$ 285,000\), and sales of \(\$ 475,000\). Carlos's days in inventory is: a. 73 days. c. \(102.5\) days. b. \(121.7\) days. d. \(84.5\) days.

Step-by-Step Solution

Answer

b. 121.7 days.

Step 1: Calculate Average Inventory

First, we need to calculate the average inventory. The average inventory is calculated using the formula: \[ \text{Average Inventory} = \frac{\text{Beginning Inventory} + \text{Ending Inventory}}{2} \] Substitute the given values: \[ \text{Average Inventory} = \frac{80,000 + 110,000}{2} = \frac{190,000}{2} = 95,000 \]

Step 2: Calculate Inventory Turnover Ratio

Next, calculate the Inventory Turnover Ratio. This measures how many times inventory is sold and replaced over a period. The formula is: \[ \text{Inventory Turnover Ratio} = \frac{\text{Cost of Goods Sold}}{\text{Average Inventory}} \] Substitute the given values: \[ \text{Inventory Turnover Ratio} = \frac{285,000}{95,000} \approx 3.00 \]

Step 3: Calculate Days in Inventory

Finally, calculate the Days in Inventory, which indicates the average number of days inventory is held before it is sold. Use the formula: \[ \text{Days in Inventory} = \frac{365}{\text{Inventory Turnover Ratio}} \] Substitute the value from the previous step: \[ \text{Days in Inventory} = \frac{365}{3.00} \approx 121.67 \]

Key Concepts

Days in Inventory

Days in Inventory is a key measure in inventory management. It tells us how long, on average, it takes for a company to sell its entire inventory during a specified period, typically a year. A higher number of days might suggest slow sales or overstocking, while a lower count suggests faster turnover. This metric is crucial for understanding the liquidity and efficiency of a company's inventory management system.
To compute Days in Inventory, you start with the Inventory Turnover Ratio, which we've previously calculated. The formula is: \[ \text{Days in Inventory} = \frac{365}{\text{Inventory Turnover Ratio}} \]Plugging in the Inventory Turnover Ratio of 3.00 results in approximately 121.67 days. This tells Carlos Company that, on average, it holds inventory for about 122 days before selling it.
Understanding the Days in Inventory can help businesses make informed decisions about purchasing and sales strategies. Efficient management systems will aim to reduce this number without compromising stock availability.

Average Inventory

Average Inventory is an important factor when dealing with inventory demands and controls. It gives a balanced view by averaging the goods available at two points in time — the beginning and the ending of the period. This makes it useful for assessing inventory levels throughout a specific period.
To find Average Inventory, use the formula: \[ \text{Average Inventory} = \frac{\text{Beginning Inventory} + \text{Ending Inventory}}{2} \]For Carlos Company, this calculation involves combining the beginning inventory of \(80,000 and the ending inventory of \)110,000, then dividing by 2. This yields an Average Inventory of $95,000.
The average inventory can serve as a base for further analysis, like calculating the Inventory Turnover Ratio. It ensures that temporary fluctuations in stock levels do not distort the overall analysis.

Inventory Turnover Ratio

The Inventory Turnover Ratio is a fascinating component of inventory management. It helps us understand how many times a company’s inventory is sold and replenished over a certain period. This ratio can indicate how efficiently a company is managing its stock and how well it meets customer demand without having excess supply.
To calculate this ratio, use the formula below: \[ \text{Inventory Turnover Ratio} = \frac{\text{Cost of Goods Sold}}{\text{Average Inventory}} \]In the scenario of Carlos Company, you take the Cost of Goods Sold (COGS), which is \(285,000, and divide it by the Average Inventory of \)95,000, resulting in a turnover ratio of approximately 3.00.
This means the inventory "turned over" 3 times during the period. A higher turnover suggests good sales or effective inventory management, whereas a lower turnover indicates the opposite. Monitoring this ratio can help businesses adjust their inventory purchases and improve cash flow.