FIFO and LIFO costs under perpetual inventory system

Question

The following units of an item were available for sale during the year:

Line Item Description Units and Cost
Beginning inventory 20 units at $46
Sale 13 units at $69
First purchase 24 units at $48
Sale 12 units at $70
Second purchase 27 units at $49
Sale 20 units at $72
The firm uses the perpetual inventory system, and there are 26 units of the item on hand at the end of the year.

a. What is the total cost of the ending inventory according to FIFO?
fill in the blank 1 of 2$

b. What is the total cost of the ending inventory according to LIFO?
fill in the blank 2 of 2$

Answer 1

To calculate the total cost of the ending inventory for both FIFO (First In, First Out) and LIFO (Last In, First Out) methods under a perpetual inventory system, we first need to analyze the transactions and the inventory remaining at the end of the year.

Inventory Transactions Summary:

1. Beginning inventory: 20 units at $46
2. Sale 1: 13 units sold
3. First purchase: 24 units at $48
4. Sale 2: 12 units sold
5. Second purchase: 27 units at $49
6. Sale 3: 20 units sold

Calculate Ending Inventory:

1. Total available units = Beginning Inventory + Purchases - Total Sales
   • Beginning Inventory: 20
   • Purchases: 24 (from first purchase) + 27 (from second purchase) = 51
   • Total Sales = 13 + 12 + 20 = 45
   • Total available units = 20 + 51 - 45 = 26 units (this matches given ending inventory).

a. Ending Inventory Cost under FIFO

Under FIFO, the earliest costs are used first. We take the last purchases into account to calculate the ending inventory cost.

1. Sales summary:
   • Sale 1: 13 units sold (from beginning inventory: 7 remaining at $46)
   • Sale 2: 12 units sold (all sold from the first purchase, leaving 12 remaining at $48)
   • Sale 3: 20 units sold (sold from the first and second purchases)

Remaining Inventory after Sales:

• From Beginning Inventory: 7 units at $46 (20 - 13 = 7 left)
• From First Purchase: 12 units at $48 (24 - 12 = 12 left)
• From Second Purchase: 27 units at $49, but sold 20 (20 of those + none from first purchase sold)
• Therefore, there will be remaining inventory.

Calculate the remaining units:

• Remaining from First Purchase: 0 units (as 24 - 12 sold = 12 and 12 used in sale 3).
• Remaining from Second Purchase: 7 units at $49 (27 - 20 = 7 left) and all existing from beginning inventory.

Total Cost under FIFO:

• \[(7 \text{ units} \times $46) + (12 \text{ units} \times $48) + (7 \text{ units} \times $49)\]
• = \(7 \times 46 + 12 \times 48 + 7 \times 49\)
• = \(322 + 576 + 343 = 1241\)

So, the total cost of ending inventory under FIFO is $1,241.

b. Ending Inventory Cost under LIFO

Under LIFO, the most recent costs (the latest purchases) are used first. We take into account the ending inventory reflecting the earliest costs first for any remaining inventory.

Remaining Inventory after Sales:

1. We will allocate units from the last purchase first.
2. Sale 3 was covered using their last units.
3. Therefore:
   • From Second Purchase: 7 units at $49
   • Remaining from First Purchase / Note: All utilized.

Costs will be reflected in the following units:

• Total Calculation:
• \[(7 \text{ units} \times $49) + (19 \text{ units} \text{ available from earlier purchases})\]
• ${ 0*? }$ as everything got exhausted.

Total Cost under LIFO:

• \[( 7 \text{ units} \times $49) + (19 remaining \text{ at } $46)\]
• = \(343 + 0\): only 49 used and units were exhausted.

Therefore:

So, the total cost of ending inventory under LIFO is $1,115.

Final Answers: a. Total Cost of Ending Inventory (FIFO): $1,241
b. Total Cost of Ending Inventory (LIFO): $1,115