Question

The following units of an item were available for sale during the year:Beginning inventory 21 units at $42Sale14 units at $65First purchase18 units at $44Sale6 units at $66Second purchase 24 units at $47Sale21 units at $67The firm uses the perpetual inventory system, and there are 22 units of the item on hand atthe end of the year.a. What is the total cost of the ending inventory according to FIFO?b. What is the total cost of the ending inventory according to LIFO?

Answer 1

As we are only interested in the cost, we will ignore the sale price, only purchase prices.

The movements are:

1) We have an initial inventory of 21 units at $42 each.

2) Sale of 14 units, so the inventory is reduced by 14 units.

3) Purchase of 18 units at $44, so the inventory is increased by 18 units.

4) Sale of 6 units, so the inventory is reduced by 6 units.

5) Purchase of 24 units at $47.

6) Sale of 21 units.

The ending inventory after this movements is 22 units.

We can calculate the cost in a FIFO system by substracting the sold units from the group that was first purchased.

In this case, we can calculate the cost as:

1) We have 21 units at $42.

2) The first sale is of 14 units, so they have a cost of 14 units of $42 each. The stock is now: 21-14 = 7 units at $42.

3) We increase the inventory by 18 units at $44, so the stock is now: 7 units at $42 and 18 untis at $44.

4) The sale of 6 units can still be satisfied with the original inventory of 7 units at $42, so the cost is 6 units at $42 each. Now the stock is: 1 unit at $42 and 18 units at $44.

5) Purchase of 24 units at $47. So the stock is now: 1 unit at $42, 18 units at $44 and 24 units at $47.

6) Sale of 21 units. We then will take the cost of 1 unit at $42 (the last from the original inventory), 18 units at $44 and the remaining 2 units at $47.

We now can add all the cost of each unit sold as:

`\begin{gathered} C=14\cdot42+6\cdot42+(1\cdot42+18\cdot44+2\cdot47) \\ C=588+252+(42+792+94) \\ C=1768 \end{gathered}`

The total cost according to FIFO is $1768.

Now, if we use LIFO (last in, first out) we will take the inventory from the last purchase first.

1) We have 21 units at $42.

2) The first sale is of 14 units, so they have a cost of 14 units of $42 each. The stock is now: 21-14 = 7 units at $42.

3) We increase the inventory by 18 units at $44, so the stock is now: 7 units at $42 and 18 untis at $44.

4) The sale of 6 units will be substracted from the inventory purchased at $44, so we will have a cost of 6 units at $44. The stock will now be: 7 units at $42 and 12 units at $44.

5) Purchase of 24 units at $47. So the stock is now: 7 units at $42, 12 units at $44 and 24 units at $47.

6) Sale of 21 units. We then will take the cost from the units in the last purchase: 21 units at $47.

Now we can calculate the total cost as:

`\begin{gathered} C=14\cdot42+6\cdot44+21\cdot47 \\ C=588+264+987 \\ C=1839 \end{gathered}`

The total cost according to LIFO is $1839.

Answer:

a) The total cost according to FIFO is $1768.

b) The total cost according to LIFO is $1839.