Question

richmond corporation reported the following information for its years ended 12/31/23 and 12/31/24:

	2023	2024
net purchases	323,000	320,300
ending inventory	?	21,500
cost of goods sold	321,500	316,100

q. what was richmonds beginning inventory at 1/1/2023?

$10,600
$15,800
$17,300
$10,900

Explanation:

Step1: Recall cost - of - goods - sold formula

The formula for cost of goods sold (COGS) is $COGS=\text{Beginning Inventory}+\text{Net Purchases}-\text{Ending Inventory}$. We want to find the beginning inventory for 2023. Rearranging the formula for beginning inventory gives $\text{Beginning Inventory}=\text{COGS}+\text{Ending Inventory}-\text{Net Purchases}$.

Step2: Identify values for 2023

For 2023, we know that $\text{COGS} = 321500$, $\text{Net Purchases}=323000$, and assume ending inventory of 2023 is the beginning inventory of 2024. We don't have the ending inventory of 2023 directly, but we can use the 2024 data to work backward if needed. First, using the 2023 data only, substituting the values into the formula: $\text{Beginning Inventory}_{2023}=321500 + \text{Ending Inventory}_{2023}-323000$.
Let's assume we can use the fact that we don't have other information and we might consider the relationship in a simple way. If we assume the problem has enough information within the 2023 data set, we substitute the values into the formula:
\[

$$\begin{align*} \text{Beginning Inventory}_{2023}&=321500+ \text{Ending Inventory}_{2023}-323000\\ \end{align*}$$

\]
We assume the ending inventory of 2023 is calculated in a way that we can use the basic formula. Since we are not given any other complex relationship, we use the formula $\text{Beginning Inventory}_{2023}=321500 + 10900-323000$ (by trial - and - error checking the options).
\[

$$\begin{align*} \text{Beginning Inventory}_{2023}&=321500+10900 - 323000\\ &=332400-323000\\ &=9400 \end{align*}$$

\]
This is wrong. Let's use the correct formula with the right logic.
We know that for 2023:
\[

$$\begin{align*} \text{Beginning Inventory}_{2023}&=\text{COGS}_{2023}+\text{Ending Inventory}_{2023}-\text{Net Purchases}_{2023}\\ \end{align*}$$

\]
We assume the ending inventory of 2023 is the beginning inventory of 2024. We first find the beginning inventory of 2024 using the 2024 data:
\[

$$\begin{align*} \text{Beginning Inventory}_{2024}&=\text{COGS}_{2024}+\text{Ending Inventory}_{2024}-\text{Net Purchases}_{2024}\\ &=316100 + 21500-320300\\ &=337600 - 320300\\ &=17300 \end{align*}$$

\]
Now for 2023:
\[

$$\begin{align*} \text{Beginning Inventory}_{2023}&=\text{COGS}_{2023}+\text{Ending Inventory}_{2023}-\text{Net Purchases}_{2023}\\ &=321500+17300 - 323000\\ &=338800-323000\\ &=15800 \end{align*}$$

\]

Answer:

$15,800$