Problem 17 - Accounting Principles

Question

(LO 6) King Company has sales of \(\$ 150,000\) and cost of goods available for sale of \(\$ 135,000\). If the gross profit rate is \(30 \%\), the estimated cost of the ending inventory under the gross profit method is: a. \(\$ 15,000\). c. \(\$ 45,000\). b. \(\$ 30,000\). d. \(\$ 75,000\).

Step-by-Step Solution

Answer

The estimated cost of the ending inventory is $30,000.

Step 1: Calculate Gross Profit

To calculate the gross profit, multiply the sales by the gross profit rate. The gross profit is given by:\[ \text{Gross Profit} = \text{Sales} \times \text{Gross Profit Rate} = 150,000 \times 0.30 = 45,000 \]

Step 2: Calculate Cost of Goods Sold (COGS)

Subtract the gross profit from sales to determine the cost of goods sold. The COGS is:\[ \text{COGS} = \text{Sales} - \text{Gross Profit} = 150,000 - 45,000 = 105,000 \]

Step 3: Calculate Ending Inventory

Subtract the cost of goods sold from the total cost of goods available for sale to estimate the ending inventory using the gross profit method:\[ \text{Ending Inventory} = \text{Cost of Goods Available for Sale} - \text{COGS} = 135,000 - 105,000 = 30,000 \]

Key Concepts

Ending Inventory Calculation

The ending inventory calculation is a crucial step in understanding a company's financial health by analyzing how much unsold stock remains at the end of an accounting period. In the gross profit method, this calculation is simplified using the data from sales, gross profit, and the cost of goods available for sale.
In the exercise provided, King Company uses the following method:

• First, determine the Cost of Goods Sold (COGS), an essential part of this calculation.
• Next, subtract the COGS from the cost of goods available for sale. This helps estimate the unsold inventory that remains, known as the ending inventory.

For King Company, the formula is: Ending Inventory = Cost of Goods Available for Sale - COGS. This results in an ending inventory of $30,000. Understanding this process aids in evaluating how efficiently a business turns over its inventory.

Cost of Goods Sold

Cost of Goods Sold (COGS) represents the direct costs attributable to the production of the goods sold by a company. This measure is vital for determining how well a company manages its costs related to production. The COGS is calculated by subtracting the gross profit from total sales.
For King Company, the calculation is straightforward:

• Sales revenue is $150,000.
• Gross Profit is calculated as $45,000.
• This makes COGS = Sales - Gross Profit, which results in $105,000.

COGS provides insights into the cost versus sales relationship. It's directly linked to pricing strategies and inventory management, influencing the overall profitability of a company.

Gross Profit Rate

The gross profit rate is a percentage that represents the portion of sales revenue that exceeds the cost of goods sold. It's an indicator of a company's ability to cover costs and generate earnings from each sale. To determine this rate, the following formula is used: Gross Profit Rate = Gross Profit / Sales.
In this specific problem for King Company:

• The sales figure is $150,000.
• With a gross profit of $45,000, the gross profit rate is calculated as $45,000 / $150,000, which is 0.30 or 30%.

A 30% gross profit rate signifies that King Company retains 30% of its sales revenue after covering the cost of goods sold. This rate helps in gauging pricing strategies and operational efficiency. A higher gross profit rate may indicate better profit margins, which is crucial for business sustainability.