Problem 8 - Accounting

Question

The units of an item available for sale during the year were as follows: \(\begin{array}{lll}\text { Jan. } 1 & \text { Inventory } & 27 \text { units at } \$ 120 \\ \text { Feb. } 17 & \text { Purchase } & 54 \text { units at } \$ 138 \\ \text { July } 21 & \text { Purchase } & 63 \text { units at } \$ 156 \\ \text { Nov. } 23 & \text { Purchase } & 36 \text { units at } \$ 165\end{array}\) There are 50 units of the item in the physical inventory at December 31 . The periodic inventory system is used. Determine the inventory cost by (a) the first-in, first-out method, (b) the last-in, first-out method, and (c) the average cost method.

Step-by-Step Solution

Answer

FIFO: $8124, LIFO: $6414, Average Cost: $7350.

Step 1: Understanding FIFO Method

The First-In, First-Out (FIFO) method assumes that the earliest goods purchased are the first to be sold. Therefore, the remaining inventory is made up of the most recently purchased items.

Step 2: Apply FIFO Method to Find Ending Inventory

Starting with the most recent purchase, we calculate the cost of remaining units: - 36 units from Nov. 23 at \\(165 each = \( 36 \times 165 = 5940 \) - 14 units from July 21 at \\)156 each = \( 14 \times 156 = 2184 \) Total cost of 50 units = \( 5940 + 2184 = 8124 \).

Step 3: Understanding LIFO Method

The Last-In, First-Out (LIFO) method assumes that the most recent goods purchased are the first to be sold. Therefore, the remaining inventory is made up of the earliest purchased items.

Step 4: Apply LIFO Method to Find Ending Inventory

Starting with the earliest inventory:- 27 units from Jan. 1 at \\(120 each = \( 27 \times 120 = 3240 \)- 23 units from Feb. 17 at \\)138 each = \( 23 \times 138 = 3174 \)Total cost of 50 units = \( 3240 + 3174 = 6414 \).

Step 5: Understanding Average Cost Method

The Average Cost method calculates the cost of ending inventory based on the average cost of all units available during the period.

Step 6: Calculate Average Unit Cost

1. Calculate the total cost of goods available for sale: - Jan. 1: \( 27 \times 120 = 3240 \) - Feb. 17: \( 54 \times 138 = 7452 \) - July 21: \( 63 \times 156 = 9828 \) - Nov. 23: \( 36 \times 165 = 5940 \) - Total cost = \( 3240 + 7452 + 9828 + 5940 = 26460 \). - Total units = \( 27 + 54 + 63 + 36 = 180 \).2. Calculate the average unit cost: - \( \text{Average unit cost} = \frac{26460}{180} = 147 \).

Step 7: Apply Average Cost Method to Find Ending Inventory

Multiply the average unit cost by the number of ending inventory units:- Cost of 50 units = \( 50 \times 147 = 7350 \).

Key Concepts

FIFO Method

The First-In, First-Out (FIFO) method is a commonly used inventory valuation approach. This method operates under the assumption that the earliest items acquired or produced are the first ones to be used or sold. As a result, the inventory left at the end of the period consists of the most recently acquired goods. This approach is intuitive, as it mimics the natural flow of inventory in many businesses, ensuring older stock doesn't become obsolete.

To apply FIFO, the cost of ending inventory is calculated by using the costs of the latest batch of goods. In the exercise, sales and other disposals are accounted for from the oldest inventory first, meaning the remaining 50 units are derived from the last batches of purchases. Given the detailed calculation, the cost of the remaining 50 units in the inventory ends up being $8,124, composed of the final 36 units from the November purchase and 14 units from the July purchase.

• Ensures actual flow of goods is mirrored.
• Can lead to higher taxes in times of rising prices, as older, cheaper goods are recorded as cost of goods sold.
• Ending inventory reflects recent purchase prices.
• Provides a reasonable match of cost against current revenue.

LIFO Method

The Last-In, First-Out (LIFO) method of inventory valuation assumes that the last items acquired are the first to be sold. This approach means that the costs associated with the most recently purchased items are used to calculate the cost of goods sold, while older inventory costs remain on the balance sheet as ending inventory. This technique is often utilized in industries where products are non-perishable and market conditions drive the costs upwards.

Implementing the LIFO method in the given problem, the ending inventory cost is calculated utilizing the oldest batch of goods. Starting with the earliest purchases means that the first 27 units of the ending inventory cost originate from January, with the subsequent 23 units coming from February. In this scenario, the total cost of ending inventory is valued at $6,414.

• Highlights more recent cost, which may better reflect economic costs.
• In inflationary times, LIFO results in higher cost of goods sold and lower taxes.
• May not match specific identification effectively in every business.
• Ending inventory can consist of older, possibly outdated costs.

Average Cost Method

The Average Cost method provides a straightforward and balanced way to handle inventory valuation by using the average cost of all items available for sale during a particular period. Unlike FIFO and LIFO, this method smooths out the valuation by factoring in cost fluctuations, which helps in stabilizing the results on financial statements.

To deploy this method, the first step is calculating the total cost of all units available for sale, then dividing this total cost by the total number of units, resulting in the average cost per unit. In the exercise, we found that the average unit cost is $147. Applying this to the 50 units remaining in the inventory, the final inventory valuation amounts to $7,350.

• Provides simplicity and ease of calculation.
• Helps normalize cost variations over time.
• May not perfectly align with economic realities of inventory costs.
• Useful when inventory items are not easily distinguishable.

Periodic Inventory System

A periodic inventory system is an accounting method where the inventory count and valuation are updated at specific intervals, such as monthly or annually, rather than continuously. At these intervals, a physical count is conducted to determine the amount of inventory on hand and adjust for sales, losses, or other changes.

In this scenario, the periodic inventory system helps identify the ending inventory balance at the end of the year, using the three methods discussed: FIFO, LIFO, and Average Cost. By applying these at the same time, the periodic nature ensures cost calculations are based on a complete snapshot rather than ongoing amounts, allowing for a broad perspective on inventory metrics.

• Offers reduced administrative burden compared to perpetual systems.
• Useful for businesses where exact inventory matches are not critical.
• Potential for discrepancies between physical count and book records.
• Provides comprehensive insight at specific intervals to aid decision making.