Chapter 5, Problem 7E

To determine

Inventory:

Inventory refers to the stock or goods which will be sold in the near future and thus is an asset for the company. It comprises of the raw materials which are yet to be processed, the stock which is still going through the process of production and it also includes completed products that are ready for sale. Thus inventory is the biggest and the important source of income and profit for the business.

Perpetual Inventory System:

In perpetual inventory system, there is a continuous recording of transactions as and when they take place that is purchase and sale transactions are recorded whenever they occur.

Cost of Goods Sold:

Cost of goods sold is the total expenses or the cost incurred by the business during the process of manufacturing of goods and is directly related to the production. It generally includes the cost of raw material, labor and other manufacturing support costs.

First In First Out: In case of First in, first out method, also known as FIFO method, the inventory which was bought first will also be the first one to be taken out.

Last In First Out: In case of Last in, First out, also known as LIFO method, the inventory which was bought in the last will be taken out first.

The cost assigned to ending inventory, cost of goods sold and gross margin as per the perpetual inventory system under the following methods:
(a) FIFO
(b) LIFO

Explanation of Solution

Date	Particulars	Units acquired	Cost per unit ($)	Cost of goods available ($)	Units sold	Retail price per unit ($)
Jan 1	Beginning inventory	200	10	2,000
Jan 10	Sales				150	40
Mar 14	Purchase	350	15	5,250
Mar 15	Sales				300	40
July 30	Purchase	450	20	9,000
Oct 5	Sales				430	40
Oct 26	Purchases	100	25	2,500
	Total	1,100		18,750	880

(a)

First in, First out method (FIFO)

Cost of the Ending inventory

Date	Purchases	Cost of goods sold	Ending inventory
Quantities (units)	Unit cost ($)	Total cost ($)	Quantities (units)	Unit cost ($)	Total cost ($)	Quantities (units)	Unit cost ($)	Balance ($)
Jan 1							200	10	2,000
Jan 10				150	10	1,500	50	10	500
Mar 14	350	15	5,250				$\begin{array}{l}50\\ 350\end{array}\}$	$\begin{array}{l}10\\ 15\end{array}\}$	$\begin{array}{l}\begin{array}{l}500\\ 5,250\end{array}\}\\ =5,750\end{array}$
Mar 15				$\begin{array}{l}50\\ 250\end{array}\}$	$\begin{array}{l}10\\ 15\end{array}\}$	$\begin{array}{l}\begin{array}{l}500\\ 3,750\end{array}\}\\ =4,250\end{array}$	100	15	1,500
July 30	450	20	9,000				$\begin{array}{l}100\\ 450\end{array}\}$	$\begin{array}{l}15\\ 20\end{array}\}$	$\begin{array}{l}\begin{array}{l}1,500\\ 9,000\end{array}\}\\ =10,500\end{array}$
Oct 5				$\begin{array}{l}100\\ 330\end{array}\}$	$\begin{array}{l}15\\ 20\end{array}\}$	$\begin{array}{l}\begin{array}{l}1,500\\ 6,000\end{array}\}\\ =8,100\end{array}$	120	20	2400
Oct 26	100	25	2,500				$\begin{array}{l}120\\ 100\end{array}\}$	$\begin{array}{l}20\\ 25\end{array}\}$	$\begin{array}{l}\begin{array}{l}2,400\\ 2,500\end{array}\}\\ =4,900\end{array}$

The cost of ending inventory is $4,900.

Compute cost of goods sold.

Formula to calculate cost of goods sold is,

$\mathrm{Cos}tofgoodssold=\mathrm{Cos}tofgoodsavailableforsale-\mathrm{Cos}tofendinginventory$

Substitute $18,750 for cost of goods available for sale (given) and $4,900 for cost of ending inventory (as calculated above) in the above formula.

$\begin{array}{c}\mathrm{Cos}tofgoodssold=\$18,750-\$4,900\\ =\$13,850\end{array}$

Compute gross margin.

Formula to calculate gross margin is,

$\text{Gross}\text{margin}\text{=}\text{Net}\text{sales}\text{-}\text{cost}\text{of}\text{goods}\text{sold}$

Substitute $35,200 for net sales (working notes) and $13,850 for cost of goods sold (as calculated above) in the above formula.
$\begin{array}{c}\text{Gross}\text{margin}\text{=}\$35,200\text{-}\$13,850\\ =\$21,350\end{array}$

The cost of ending inventory is $4,900 and it consists of 120 units at the rate of $20 and 100 units at the rate of $25. Also the cost of goods sold is $13,850 and gross margin is $21,350.

(b)

Last in, First out Method (LIFO)

Cost of the Ending inventory

Date	Purchases	Cost of goods sold	Ending inventory
Quantities (units)	Unit cost ($)	Total cost ($)	Quantities (units)	Unit cost ($)	Total cost ($)	Quantities (units)	Unit cost ($)	Balance ($)
Jan 1							200	10	2,000
Jan 10				150	10	1,500	50	10	500
Mar 14	350	15	5,250				$\begin{array}{l}50\\ 350\end{array}\}$	$\begin{array}{l}10\\ 15\end{array}\}$	$\begin{array}{l}\begin{array}{l}500\\ 5,250\end{array}\}\\ =5,750\end{array}$
Mar 15				300	15	4,500	$\begin{array}{l}50\\ 50\end{array}\}$	$\begin{array}{l}10\\ 15\end{array}\}$	$\begin{array}{l}\begin{array}{l}500\\ 750\end{array}\}\\ =1,250\end{array}$
July 30	450	20	9,000				$\begin{array}{l}50\\ 50\\ 450\end{array}\}$	$\begin{array}{l}10\\ 15\\ 20\end{array}\}$	$\begin{array}{l}\begin{array}{l}500\\ 750\\ 9,000\end{array}\}\\ =10,250\end{array}$
Oct 5				430	20	8,600	$\begin{array}{l}50\\ 50\\ 20\end{array}\}$	$\begin{array}{l}10\\ 15\\ 20\end{array}\}$	$\begin{array}{l}\begin{array}{l}500\\ 750\\ 400\end{array}\}\\ =10,250\end{array}$
Oct 26	100	25	2,500				$\begin{array}{l}50\\ 50\\ 20\\ 100\end{array}\}$	$\begin{array}{l}10\\ 15\\ 20\\ 25\end{array}\}$	$\begin{array}{l}\begin{array}{l}500\\ 750\\ 400\\ 2,500\end{array}\}\\ =4,150\end{array}$

Date	Receipts	Issues	Balance
Units	Rate ($)	Amount ($)	Units	Rate ($)	Amount ($)		Units	Rate ($)	Amount ($)
Jan 1							200	10	2,000
Jan 10				150	10	1,500	50	10	500
Mar 14	350	15	5,250				50 350	10 15	500 5,250
Mar 15				300	15	4,500	50 50	10 15	500 750
Jul 30	450	20	9,000				50 50 450	10 15 20	500 750 9,000
Oct 5				430	20	8,600	50 50 20	10 15 20	500 750 400
Oct 26	100	25	2,500				50 50 20 100	10 15 20 25	500 750 400 2,500

The cost of ending inventory is $4,150.

Compute cost of goods sold.

Formula to calculate cost of goods sold is,

$\mathrm{Cos}tofgoodssold=\mathrm{Cos}tofgoodsavailableforsale-\mathrm{Cos}tofendinginventory$

Substitute $18,750 for cost of goods available for sale (given) and $4,150 for cost of ending inventory (as calculated above) in the above formula.

$\begin{array}{c}\mathrm{Cos}tofgoodssold=\$18,750-\$4,150\\ =\$14,600\end{array}$

Compute gross margin.

Formula to calculate gross margin is,

$\text{Gross}\text{margin}\text{=}\text{Net}\text{sales}\text{-}\text{cost}\text{of}\text{goods}\text{sold}$

Substitute $35,200 for net sales (working notes) and $14,600 for cost of goods sold (as calculated above) in the above formula.

$\begin{array}{c}\text{Gross}\text{margin}\text{=}\$35,200\text{-}\$14,600\\ =\$20,600\end{array}$

Working notes:

$\begin{array}{c}\text{Net}\text{sales}=\text{Total}\text{number}\text{of}\text{units}\text{sold}\times \text{Price}\text{per}\text{unit}\\ =880\times \$40\\ =\$35,200\end{array}$

The closing inventory is $4,150 and it consists of 50 units at the rate of $10, 50 units at the rate of $15, 20 units at the rate of $20 and 100 units at the rate of $25. Also the cost of goods sold is $14,600 and the gross margin is $20,600.