Question

Hull Company’s record of transactions concerning part X for the month of April was as follows.

Purchases Sales

April 1 (balance on hand) 100 @ $5.00 April 5 300

4 400 @ 5.10 12 200

11 300 @ 5.30 27 800

18 200 @ 5.35 28 150

26 600 @ 5.60

30 200 @ 5.80

Instructions

(a) Compute the inventory at April 30 on each of the following bases. Assume that perpetual inventory records are kept inunits only. Carry unit costs to the nearest cent.

(1) First-in, first-out (FIFO).

(2) Last-in, first-out (LIFO).

(3) Average cost.

(b) If the perpetual inventory record is kept in dollars, and costs are computed at the time of each withdrawal, what amountwould be shown as ending inventory in (1), (2), and (3) above? (Carry average unit costs to four decimal places.)

Short answer

Ending inventory under the periodic system:

FIFO $2000

LIFO $1175

Average cost $1890

Ending inventory under the perpetual system:

FIFO $2000

LIFO $1915

Average cost $1977.3

Step-by-step solution

Valuation of ending inventory

As the inventory records are kept in units only, the FIFO, LIFO, and Average cost would be computed based on the periodic system.

$$\begin{gathered} \mathbf{Endinginventory}\mathbf{\left(}\mathbf{Units}\mathbf{\right)}\mathbf{=}\mathbf{Openingstock}\mathbf{+}\mathbf{TotalPurchases}\mathbf{-}\mathbf{TotalSales} \\ \mathbf{=}\mathbf{100}\mathbf{+}\mathbf{(}\mathbf{400}\mathbf{+}\mathbf{300}\mathbf{+}\mathbf{200}\mathbf{+}\mathbf{600}\mathbf{+}\mathbf{200}\mathbf{)}\mathbf{-}\mathbf{(}\mathbf{300}\mathbf{+}\mathbf{200}\mathbf{+}\mathbf{800}\mathbf{+}\mathbf{150}\mathbf{)} \\ \mathbf{=}\mathbf{100}\mathbf{+}\mathbf{1700}\mathbf{-}\mathbf{1450} \\ \mathbf{=}\mathbf{350} \end{gathered}$$

1) Inventory valuation under FIFO

Date	Units	Units Cost	Total Cost
April 30	200	$5.80	$1160
April 26	150	$5.60	$840
	350		$2000

2) Inventory valuation under LIFO

Date	Units	Units Cost	Total Cost
April 1	100	$5	$500
April 4	250	$5.10	$1275
	350		$1775

3) Inventory valuation under Weighted Average method

$$\begin{gathered} \mathbf{Averagecostofinventory}\mathbf{=}\frac{\mathbf{ValueofOpeningstock}\mathbf{+}\mathbf{Valueofallpurchases}}{\mathbf{Totalavailablegoods}} \\ \mathbf{=}\frac{\mathbf{(}\mathbf{100}\mathbf{\times }\mathbf{\$}\mathbf{5}\mathbf{)}\mathbf{+}\mathbf{(}\mathbf{400}\mathbf{\times }\mathbf{\$}\mathbf{5}\mathbf{.}\mathbf{10}\mathbf{+}\mathbf{300}\mathbf{\times }\mathbf{\$}\mathbf{5}\mathbf{.}\mathbf{30}\mathbf{+}\mathbf{200}\mathbf{\times }\mathbf{\$}\mathbf{5}\mathbf{.}\mathbf{35}\mathbf{+}\mathbf{600}\mathbf{\times }\mathbf{\$}\mathbf{5}\mathbf{.}\mathbf{60}\mathbf{+}\mathbf{200}\mathbf{\times }\mathbf{\$}\mathbf{5}\mathbf{.}\mathbf{80}\mathbf{)}}{\mathbf{(}\mathbf{100}\mathbf{+}\mathbf{400}\mathbf{+}\mathbf{300}\mathbf{+}\mathbf{200}\mathbf{+}\mathbf{600}\mathbf{+}\mathbf{200}\mathbf{)}} \\ \mathbf{=}\frac{\mathbf{\$}\mathbf{500}\mathbf{+}\mathbf{\$}\mathbf{9220}}{\mathbf{1800}} \\ \mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{.}\mathbf{4} \end{gathered}$$

$$\begin{gathered} \mathbf{Costofendinginventory}\mathbf{=}\mathbf{Averagecostofinventory}\mathbf{\times }\mathbf{No}\mathbf{.}\mathbf{ofendinginventory} \\ \mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{.}\mathbf{4}\mathbf{\times }\mathbf{350} \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{890} \end{gathered}$$

Valuation of ending inventory by the perpetual method

1) Inventory valuation under FIFO

Date	Purchase	Cost of goods sold	Balance
Units	Cost	Balance	Units	Cost	Balance	Units	Cost	Balance
April 1	100	$5	$500				100	$5	$500
April 4	400	$5.10	$2040				100	$5	$500
							400	$5.10	$2040
April 5				100	$5	$500
				200	$5.10	$1020	200	$5.10	$1020
April 11	300	$5.30	$1590				200	$5.10	$1020
							300	$5.30	$1590
April 12				200	$5.10	$1020	300	$5.30	$1590
April 18	200	$5.35	$1070				300	$5.30	$1590
							200	$5.35	$1070
April 26	600	$5.60	$3360				300	$5.30	$1590
							200	$5.35	$1070
							600	$5.60	$3360
April 27				300	$5.30	$1590
				200	$5.35	$1070
				300	$5.60	$1680	300	$5.60	$1680
April 28				150	$5.60	$840	150	$5.60	$840
April 30	200	$5.80	$1160				150	$5.60	$840
							200	$5.80	$1160
Total				1450		$7720	350		$2000

Ending Inventory under FIFO is $2000.

2) Inventory valuation under LIFO

Date	Purchase	Cost of goods sold	Balance
Units	Cost	Balance	Units	Cost	Balance	Units	Cost	Balance
April 1	100	$5	$500				100	$5	$500
April 4	400	$5.10	$2040				100	$5	$500
							400	$5.10	$2040
April 5				300	$5.10	$1530	100	5	$500
							100	$5.10	$510
April 11	300	$5.30	$1590				100	$5	$500
							100	$5.10	$510
							300	$5.30	$1590
April 12				200	$5.30	$1060	100	$5	$500
							100	$5.10	$510
							100	$5.30	$530
April 18	200	$5.35	$1070				100	$5	$500
							100	$5.10	$510
							100	$5.30	$530
							200	$5.35	$1070
April 26	600	$5.60	$3360				100	$5	$500
							100	$5.10	$510
							100	$5.30	$530
							200	$5.35	$1070
							600	$5.60	$3360
April 27				600	$5.60	$3360	100	$5	$500
				200	$5.35	$1070	100	$5.10	$510
							100	$5.30	$530
April 28				100	$5.30	$530	100	$5	$500
				50	$5.10	$255	50	$5.10	$255
April 30	200	$5.80	$1160				100	$5	$500
							50	$5.10	$255
							200	$5.80	$1160
Total				1450		$7805	350		$1915

Ending inventory under FIFO is $1915

3) Inventory valuation under weighted average method.

Date	Purchase	Cost of goods sold	Balance
Units	Cost	Balance	Units	Cost	Balance	Units	Cost	Balance
April 1	100	$5	$500				100	$5	$500
April 4	400	$5.10	$2040				100	$5	$500
							400	$5.10	$2040
Total							500	$5.08	$2540
April 5				300	$5.08	$1524	200	$5.08	$1016
April 11	300	$5.30	$1590				200	$5.08	$1016
							300	$5.30	$1590
Total							500	$5.212	$2606
April 12				200	$5.212	$1042.4	300	$5.212	$1563.6
April 18	200	$5.35	$1070				300	$5.212	$1563.6
							200	$5.35	$1070
Total							500	$5.2672	$2633.6
April 26	600	$5.60	$3360				500	$5.2672	$2633.6
							600	$5.60	$3360
Total							1100	$5.4487	$5993.6
April 27				800	$5.4487	$4358.96	300	$5.4487	$1634.61
April 28				150	$5.4487	$817.305	150	$5.4487	$817.305
April 30	200	$5.80	$1160				150	$5.4487	$817.30
							200	$5.80	$1160
Total				1450		$7742.665	350	$5.6494	$1977.3

Ending inventory under the average method is $1977.3.