Chapter 5, Problem 1PSB

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 Available for Sale

It basically includes the cost of inventory which is ready for sale within an accounting period. It mainly includes the cost of beginning inventory as well as the stock purchased in that year and the production within that period (if any).

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.

Gross Profit

The profit made after subtracting or debiting the costs related to the goods sold from the total revenue earned or made through sales in a fiscal year is the gross profit.

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.

Weighted Average Cost Method

In this method the weighted average cost is evaluated after any purchases have been made and transactions are recorded as when purchase or sales take place.

Specific Identification Method

Under this method, there is a continuous tracking of the inventory and the inventory cost at the time of purchase on the basis of unique identity which thus helps in the valuation of the ending inventory as well as the cost of goods sold. This method is used generally when the company is involved in limited expensive goods which are easily identifiable.

To compute: 1. Cost of goods available for sale and number of units available for sale.
2. Number of units in ending inventory.
3. Cost of ending inventory under the following methods:

(a) FIFO
(b)LIFO
(c) Weighted average
(d) Specific identification

4. Gross profit for each of the four methods in part

Given info,

Date	Particulars	Units acquired	Cost per unit ($)	Units sold	Retail price per unit ($)
Apr 1	Beginning inventory	20	3,000
Apr 6	Purchase	30	3,500
Apr 9	Sales			35	12,000
Apr 17	Purchase	5	4,500
Apr 25	Purchase	10	4,800
Apr 30	Sales			25	14,000
	Total	65		60

The ending inventory consists of 5 units from April 17.

Explanation of Solution

1.

Cost of goods available for sale

Formula to calculate Cost of goods available for sale is,

$\text{Cost}\text{of}\text{goods}\text{available}\text{for}\text{sale}=\text{Beginning}\text{inventory}-\text{Purchases}$

Cost and units of goods available for sale:

Particulars	Number of units $$	Cost per unit ($)	Amount ($) $\left(\left(\text{Number}\text{of}\text{units}\right)\times \left(\text{Cost}\text{per}\text{unit}\right)\right)$
Beginning Inventory $\left(A\right)$	20	3000	60,000
Purchases:
April 6	30	3,500	105,000
April 17	5	4,500	22,500
April 25	10	4,800	48,000
Total Purchases $\left(B\right)$	45		175,500
Available for sale $\left(A+B\right)$	65		235,500
Table (1)

The cost of goods available for sale is $235,500 and the number of units available for sale is 740 units.

(2)

Number of units in ending inventory

Particulars	Number of units
Number of units available for sale (given)	65
Less: units sold (given)	60
Number of units in ending inventory	5
Table (2)

The number of units in ending inventory is 5 units.

3.

(a)

First in, First out method (FIFO)

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 ($)	Balance ($)
Apr 1.							20	3,000	60,000
Apr 6	30	3,500	105,000				$\begin{array}{l}20\\ 30\end{array}\}$	$\begin{array}{l}3,000\\ 3,500\end{array}\}$	$\begin{array}{l}\begin{array}{l}60,000\\ 105,000\end{array}\}\\ =165,000\end{array}$
Apr 9				$\begin{array}{l}20\\ 15\end{array}\}$	$\begin{array}{l}3,000\\ 3,500\end{array}\}$	$\begin{array}{l}\begin{array}{l}60,000\\ 52,500\end{array}\}\\ =112,500\end{array}$	15	3,500	52,500
Apr 17	5	4,500	22,500				$\begin{array}{l}15\\ 5\end{array}\}$	$\begin{array}{l}3,500\\ 4,500\end{array}\}$	$\begin{array}{l}\begin{array}{l}52,500\\ 22,500\end{array}\}\\ =75,000\end{array}$
Apr 25	10	4,800	48,000				$\begin{array}{l}15\\ 5\\ 10\end{array}\}$	$\begin{array}{l}3,500\\ 4,500\\ 4,800\end{array}\}$	$\begin{array}{l}\begin{array}{l}52,500\\ 22,500\\ 48,000\end{array}\}\\ =123,000\end{array}$
Apr 30				$\begin{array}{l}15\\ 5\\ 5\end{array}\}$	$\begin{array}{l}3,500\\ 4,500\\ 4,800\end{array}\}$	$\begin{array}{l}\begin{array}{l}52,500\\ 22,500\\ 24,000\end{array}\}\\ =99,000\end{array}$	5	4,800	24,000
Table (4)

Cost of goods sold

Formula to calculate cost of goods sold is,

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

Substitute $235,500for cost of goods available for sale (calculated in part (1)) and $24,000 for cost of ending inventory (as calculated above in the table) in the above formula.

$\begin{array}{c}\mathrm{Cos}tofgoodssold=\$235,500-\$24,000\\ =\$211,500\end{array}$

Under FIFO method, the amount of ending inventory is $24,000 and cost of goods sold is $211,500.

(b)

Last in, first out method (LIFO)

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 ($)	Balance ($)
Apr 1.							20	3,000	60,000
Apr 6	30	3,500	105,000				$\begin{array}{l}20\\ 30\end{array}\}$	$\begin{array}{l}3,000\\ 3,500\end{array}\}$	$\begin{array}{l}\begin{array}{l}60,000\\ 105,000\end{array}\}\\ =165,000\end{array}$
Apr 9				$\begin{array}{l}30\\ 5\end{array}\}$	$\begin{array}{l}3,500\\ 3,000\end{array}\}$	$\begin{array}{l}\begin{array}{l}105,000\\ 15,000\end{array}\}\\ =120,000\end{array}$	15	3,000	45,000
Apr 17	5	4,500	22,500				$\begin{array}{l}15\\ 5\end{array}\}$	$\begin{array}{l}3,000\\ 4,500\end{array}\}$	$\begin{array}{l}\begin{array}{l}45,000\\ 22,500\end{array}\}\\ =67,500\end{array}$
Apr 25	10	4,800	48,000				$\begin{array}{l}15\\ 5\\ 10\end{array}\}$	$\begin{array}{l}3,000\\ 4,500\\ 4,800\end{array}\}$	$\begin{array}{l}\begin{array}{l}45,000\\ 22,500\\ 48,000\end{array}\}\\ =115,500\end{array}$
Apr 30				$\begin{array}{l}10\\ 5\\ 10\end{array}\}$	$\begin{array}{l}4,800\\ 4,500\\ 3,000\end{array}\}$	$\begin{array}{l}\begin{array}{l}48,000\\ 22,500\\ 30,000\end{array}\}\\ =100,500\end{array}$	5	3,000	15,000
Table (6)

Cost of goods sold

Formula to calculate cost of goods sold is,

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

Substitute $235,500for cost of goods available for sale (calculated in part (1)) and $15,000 for cost of ending inventory (as calculated above in the table) in the above formula.

$\begin{array}{c}\mathrm{Cos}tofgoodssold=\$235,500-\$15,000\\ =\$220,500\end{array}$

Under LIFO method, the amount of ending inventory is $15,000 and cost of goods sold is $220,500.

(c)

Weighted Average Method

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 ($)	Balance ($)
Apr 1.							20	3,000	60,000
Apr 6	30	3,500	105,000				50	3,300	165,000
Apr 9				35	3,300	115,500	15	3,300	49,500
Apr 17	5	4,500	22,500				20	3,600	72,000
Apr 25	10	4,800	48,000				30	4,000	120,000
Apr 30				25	4,000	100,000	5	4,000	20,000
Table (8)

Working Notes:

Calculation of weighted average cost per unit:

$WeightedAverage\mathrm{Cos}tperunit=\frac{\mathrm{Cos}tofgoodsavailableforsale}{Numberofunitsavailable}$

$\begin{array}{c}Weightedaverage\cos tperunit(asonApril6)=\left(\frac{\$3,000\times 20+\$3,500\times 30}{20units+30units}\right)\\ =\left(\frac{\$165,000}{50}\right)\\ =\$3,300perunit\end{array}$

$\begin{array}{c}Weightedaverage\cos tperunit(asonApril17)=\left(\frac{\$3,300\times 15+\$4,500\times 5}{15units+5units}\right)\\ =\left(\frac{\$72,000}{20}\right)\\ =\$3,600perunit\end{array}$

$\begin{array}{c}Weightedaverage\cos tperunit(asonApril25)=\left(\frac{\$3,600\times 20+\$4,800\times 10}{20units+10units}\right)\\ =\left(\frac{\$120,000}{30}\right)\\ =\$4,000perunit\end{array}$

Cost of goods sold

Formula to calculate cost of goods sold is,

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

Substitute $235,500for cost of goods available for sale (calculated in part (1)) and $20,000 for cost of ending inventory (as calculated above in the table) in the above formula.

$\begin{array}{c}\mathrm{Cos}tofgoodssold=\$235,500-\$20,000\\ =\$215,500\end{array}$

Under weighted average method, the amount of ending inventory is $20,000 and cost of goods sold is $215,500.

(d)

Specific identification method

Given info,
The ending inventory consists of 5 units from April 17.

Cost of Ending Inventory

Date of Purchase	Number of units (A)	Cost per unit ($) (B)	Amount ($) $\left(\left(A\right)\times \left(B\right)\right)$
April 17	5	4,500	22,500
Cost of Ending Inventory			22,500
Table (9)

Cost of goods sold

Formula to calculate cost of goods sold is,

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

Substitute $235,500for cost of goods available for sale (calculated in part (1)) and $22,500 for cost of ending inventory (calculated above in the table) in the above formula.

$\begin{array}{c}\mathrm{Cos}tofgoodssold=\$235,500-\$22,500\\ =\$213,000\end{array}$

The cost of ending inventory is $22,500 and the cost of goods sold is $213,000.

4.
Sales are $770,000 (working notes).
Cost of goods sold in case of FIFO is $211,500. (Calculated in part (3(a))
Cost of goods sold in case LIFO is $220,500.(Calculated in part (3(b))
Cost of goods sold in case of weighted average is $215,500 and (Calculated in part (3(c))
Cost of goods sold in case of specific identification is 213,000.(Calculated in part (3(d))

Gross Profit

Formula to calculate gross profit is,

$\begin{array}{l}\text{Gross}\text{Profit}=\text{Sales}-\text{Cost}\text{of}\text{goods}\text{sold}\\ \end{array}$

Particulars	FIFO	LIFO	Weighted average	Specific identification
Sales(working notes)	$770,000	$$770,000	$770,000	$770,000
Less: Cost of goods sold	$211,500	$220,500	$215,500	$213,000
Gross profit	$558,500	$549,500	$554,500	$557,000
Table (10)

Working notes:

Calculation of sales

$\begin{array}{c}\text{Sales}\text{as}\text{on}\text{April}9=\text{Number}\text{of}\text{units}\text{sold}\times \text{cost}\text{per}\text{unit}\\ =35\times \$12,000\\ =\$420,000\end{array}$

$\begin{array}{c}\text{Sales}\text{as}\text{on}\text{April}30=\text{Number}\text{of}\text{units}\text{sold}\times \text{cost}\text{per}\text{unit}\\ =25\times \$14,000\\ =\$350,000\end{array}$

$\begin{array}{c}\text{Sales}=\text{Sales}\text{as}\text{on}\text{April}\text{9}+\text{Sales}\text{as}\text{on}\text{April}\text{30}\\ \text{=\$420,000+\$350,000}\\ \text{=\$770,000}\\ \end{array}$

The gross profit in case of FIFO it is $558,500, of LIFO it is $549,500, of weighted average it is $554,500 and of specific identification it is $557,000.