Chapter 5, Problem 2PSA

Periodic: Alternative cost flows $\text{P}3$
Refer to the information in Problem 5-1A and assume the periodic inventory system is used.
Required

1. Compute cost of goods available for sale and the number of units available for sale.
2. Compute the number of units in ending inventory.
3. Compute the cost assigned to ending inventory using(a) FIFO,(b) LIFO, (c) weighted average, and (d) specific identification. (Round all amounts to cents.)
4. Compute gross profit earned by the company for each of the four costing methods in part 3.

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.

Periodic inventory system: In periodic inventory system the changes in the stock items are reported periodically unlike recording as and when purchases or sales take place.

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.

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.

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.

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.

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 3.

Explanation of Solution

Given info,

Units available for sale are 820 units.

Units of goods sold are 580 units.

(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 $\left(A\right)$	100	50	5,000
Purchases:
March 5	400	55	22,000
March 18	120	60	7,200
March 25	200	62	12,400
Total Purchases $\left(B\right)$	720		41,600
Available for sale $\left(A+B\right)$	820		46,600

Conclusion

The cost of goods available for sale is $46,600 and the number of units available for sale is 820 units.

(2)

Number of units in ending inventory

Particulars	Number of units
Number of units available for sale (given)	820
Less: units sold (given)	580
Number of units in ending inventory	240

The number of units in ending inventory is 240 units.

(3)

(a)

First in First out method (FIFO)

Cost of ending inventory

Particulars	Amount($)
Most recent cost; March 25:
200 units @ $62 per unit	12,400
Next most recent cost; March 18:
40 units @ $60 per unit	2,400
Total cost of the ending inventory	14,800

Cost of goods sold

Formula to calculate cost of goods sold is,

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

Substitute $46,600 for cost of goods available for sale (calculated above in (1) part) and $14,800 for cost of ending inventory (as calculated above in the table) in the above formula.

  $\begin{array}{c}\mathrm{Cos}tofgoodssold=\$46,600-\$14,800\\ =\$31,800\end{array}$

The cost of ending inventory is 14,800 and the cost of goods sold is $31,800.

(b)

Last in First out method (LIFO)

Cost of ending inventory

Particulars	Amount($)
Earliest cost; March 1:
100 units @ $50 per unit	5,000
Next earliest cost; March 5:
140 units @ $55 per unit	7,700
Total cost of the ending inventory	12,700

Cost of goods sold

Formula to calculate cost of goods sold is,

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

Substitute $46,600 for cost of goods available for sale (calculated in (1) part) and $12,700 for cost of ending inventory (as calculated above in the table) in the above formula.

  $\begin{array}{c}\mathrm{Cos}tofgoodssold=\$46,600-\$12,700\\ =\$33,900\end{array}$

The cost of ending inventory is $12,700 and the cost of goods sold is $33,900.

(c)

Weighted Average method

Cost of ending inventory

Formula to calculate cost of ending inventory is,

  $\mathrm{Cos}tofendinginventory=\left(\begin{array}{l}Unitsinendinginventory\\ \times weightedaverage\cos tperunit\end{array}\right)$

Substitute 240 units for units in ending inventory (calculated in the (2) part) and $2.57 for weighted average cost per unit (working notes).in the above formula.

  $\begin{array}{c}\mathrm{Cos}tofendinginventory=240\times \$56.83\\ =\$13,639.2\end{array}$

Cost of goods sold

Formula to calculate cost of goods sold is,

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

Substitute $46,600 for cost of goods available for sale (calculated in the (1) part) and $13,639.2 for cost of ending inventory (as calculated above) in the above formula.

  $\begin{array}{c}\mathrm{Cos}tofgoodssold=\$46,600-\$13,639.2\\ =\$32,960\end{array}$

Working Notes:

Calculation of weighted average cost per unit:

  $Weightedaverage\text{ cost}perunit=\frac{\mathrm{Cos}tofgoodsavailableforsale}{Numberofunitsavailable}$

  $\begin{array}{c}Weightedaverage\cos tperunit=\frac{\$46,600}{820}\\ =\$56.83perunit\end{array}$

The cost of ending inventory is $13,639 and the cost of goods sold is $32,960.

(d)

Specific identification method

Given info,

The ending inventory has,

20 units are from March 1,

60 units are from March 5,

80 units are from March 18 and

80 units are from March 25.

Cost of Ending Inventory

Date of Purchase	Number of units(A)	Cost per unit($)(B)	Amount($)$\left(\left(A\right)\times \left(B\right)\right)$
March 1	20	50	1,000
March 5	60	55	3,300
March 18	80	60	4,800
March 25	80	62	4,960
Cost of ending inventory			14,060

Cost of goods sold

Formula to calculate cost of goods sold is,

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

Substitute $46,600 for cost of goods available for sale (calculated in part (1)) and $14,060 for cost of ending inventory (calculated above in the table) in the above formula.

  $\begin{array}{c}\mathrm{Cos}tofgoodssold=\$46,600-\$14,060\\ =\$32,540\end{array}$

The cost of ending inventory is $14,060 and the cost of goods sold is $32,450.

(4)

Sales are $50,900 (working notes).

Cost of goods sold in case of FIFO is $31,800. (Calculated in part (3(a))

Cost of goods sold in case LIFO is $33,400. (Calculated in part (3(b))

Cost of goods sold in case of weighted average is $32,960 and (Calculated in part (3(c))

Cost of goods sold in case of specific identification is 32,540. (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)	$50,900	$50,900	$50,900	$50,900
Less: Cost of goods sold	$31,800	$33,900	$32,960	$32,540
Gross profit	$19,100	$17,000	$17,939	$18,360

Working notes:

Calculation of sales

  $\begin{array}{c}\text{Sales}\text{as}\text{on}\text{March}\text{9}=\text{Number}\text{of}\text{units}\text{sold}\times \text{cost}\text{per}\text{unit}\\ =420\times \$85\\ =\$35,700\end{array}$

  $\begin{array}{c}\text{Sales}\text{as}\text{on}\text{March}2\text{9}=\text{Number}\text{of}\text{units}\text{sold}\times \text{cost}\text{per}\text{unit}\\ =160\times \$95\\ =\$15,200\end{array}$

  $\begin{array}{c}\text{Sales}=\text{Sales}\text{as}\text{on}\text{March}\text{9}+\text{Sales}\text{as}\text{on}\text{March}\text{29}\\ \text{=\$35,700+\$15,200}\\ \text{=\$50,900}\\ \end{array}$

The gross profit in case of FIFO method is $19,100, of LIFO method is $17,000, of weighted average is $17,939 and of specific identification it is $18,360.