You are provided with the following information for Pavey Inc. for the month ended October 31, 2008. Pavey uses a periodic method for inventory.
Date
Description
Units
Unit Cost or
Selling Price
October 1 Beginning inventory 60 $25
October 9 Purchase 120 26
October 11 Sale 100 35
October 17 Purchase 70 27
October 22 Sale 60 40
October 25 Purchase 80 28
October 29 Sale 110 40
Instructions
(a) Calculate (i) ending inventory, (ii) cost of goods sold, (iii) gross profit, and (iv) gross profit rate under each of the following methods. (Round weighted-average cost per unit to 3 decimal places and use the rounded amount for future computations. Round gross profit rate to 1 decimal place and all other answers to 0 decimal places.)
(1) LIFO.
(2) FIFO.
(3) Average-cost.
You did not finish the question.
To calculate the ending inventory, cost of goods sold (COGS), gross profit, and gross profit rate under each of the three inventory costing methods (LIFO, FIFO, and Average-cost), we need to follow these steps:
Step 1: Determine the flow of inventory
- Identify the order in which inventory was purchased and sold during the month.
Step 2: Calculate the cost of inventory sold (COGS)
- Multiply the units sold by their corresponding costs.
Step 3: Calculate the ending inventory
- Determine the remaining units of inventory on hand at the end of the month.
- Multiply these units by their corresponding costs.
Step 4: Calculate the gross profit
- Subtract the COGS from net sales to obtain gross profit.
Step 5: Calculate the gross profit rate
- Divide gross profit by net sales and multiply by 100 to get the gross profit rate as a percentage.
Let's now calculate the values for each inventory costing method.
LIFO (Last-In, First-Out):
- Under LIFO, the latest inventory purchased is assumed to be sold first.
Step 1: Determine the flow of inventory:
- Beginning inventory: 60 units (@ $25) = $1500.
- Purchase on October 9: 120 units (@ $26) = $3120.
- Purchase on October 17: 70 units (@ $27) = $1890.
- Purchase on October 25: 80 units (@ $28) = $2240.
- Sale on October 11: 100 units.
- Remaining inventory on October 31: ???
Step 2: Calculate the COGS:
- Sale on October 11: 100 units x $25 (from beginning inventory) = $2500.
Step 3: Calculate the ending inventory:
- Remaining inventory on October 31: 130 units (60 + 120 + 70 + 80 - 100) x $28 (from the latest purchase) = $3640.
Step 4: Calculate the gross profit:
- Gross profit = Net sales - COGS.
- Since net sales are not given, the calculation cannot be completed.
Step 5: Calculate the gross profit rate:
- Gross profit rate = (Gross profit / Net sales) x 100.
- Since gross profit cannot be calculated, the gross profit rate cannot be determined.
FIFO (First-In, First-Out):
- Under FIFO, the earliest inventory purchased is assumed to be sold first.
Step 1: Determine the flow of inventory:
- Beginning inventory: 60 units (@ $25) = $1500.
- Purchase on October 9: 120 units (@ $26) = $3120.
- Purchase on October 17: 70 units (@ $27) = $1890.
- Purchase on October 25: 80 units (@ $28) = $2240.
- Sale on October 11: 100 units.
- Remaining inventory on October 31: ???
Step 2: Calculate the COGS:
- Sale on October 11: 100 units x $26 (from the earliest purchase) = $2600.
Step 3: Calculate the ending inventory:
- Remaining inventory on October 31: 130 units (60 + 120 + 70 + 80 - 100) x $28 (from the latest purchase) = $3640.
Step 4: Calculate the gross profit:
- Gross profit = Net sales - COGS.
- Since net sales are not given, the calculation cannot be completed.
Step 5: Calculate the gross profit rate:
- Gross profit rate = (Gross profit / Net sales) x 100.
- Since gross profit cannot be calculated, the gross profit rate cannot be determined.
Average-cost:
- Under the average-cost method, the cost of goods available for sale is divided by the total units available for sale to get the average cost per unit.
Step 1: Determine the flow of inventory:
- Beginning inventory: 60 units (@ $25) = $1500.
- Purchase on October 9: 120 units (@ $26) = $3120.
- Purchase on October 17: 70 units (@ $27) = $1890.
- Purchase on October 25: 80 units (@ $28) = $2240.
- Sale on October 11: 100 units.
- Remaining inventory on October 31: ???
Step 2: Calculate the COGS:
- Sale on October 11: 100 units x $25 (average cost per unit) = $2500.
Step 3: Calculate the ending inventory:
- Remaining inventory on October 31: 130 units (60 + 120 + 70 + 80 - 100) x Average cost per unit.
- Average cost per unit calculation:
- Total cost of goods available for sale = $1500 + $3120 + $1890 + $2240 = $8750.
- Total units available for sale = 60 + 120 + 70 + 80 = 330 units.
- Average cost per unit = Total cost of goods available for sale / Total units available for sale = $8750 / 330 units = $26.515 (rounded to 3 decimal places).
- Remaining inventory on October 31 = 130 units x $26.515 = $3444.95 (rounded to 2 decimal places).
Step 4: Calculate the gross profit:
- Gross profit = Net sales - COGS.
- Since net sales are not given, the calculation cannot be completed.
Step 5: Calculate the gross profit rate:
- Gross profit rate = (Gross profit / Net sales) x 100.
- Since gross profit cannot be calculated, the gross profit rate cannot be determined.
Note: Calculating gross profit and gross profit rate requires the information on net sales, which is not provided in the given data.