Chapter 6, Problem 73APSA

( Appendix 6B) Inventory Costing Methods

Jet Black Products uses a periodic inventory system. For 2018 and 2019, Jet Black has the following data:

All purchases and sales are for cash.

Required:

1. Compute cost of goods sold, the cost of ending inventory, and gross margin for each year using FIFO.

2. Compute cost of goods sold, the cost of ending inventory, and gross margin for each year using LIFO.

3. Compute cost of goods sold, the cost of ending inventory, and gross margin for each year using the average cost method. ( Note: Use four decimal places for per unit calculations and round all other numbers to the nearest dollar.)

4. CONCEPTUAL CONNECTION Which method would result in the lowest amount paid for taxes?

5. CONCEPTUAL CONNECTION Which method produces the most realistic amount for income? For inventory? Explain your answer.

6. CONCEPTUAL CONNECTION What is the effect of purchases made later in the year on the gross margin when LIFO is employed? When FIFO is employed? Be sure to explain why any differences occur.

7. CONCEPTUAL CONNECTION If you worked Problem 6-68A, compare your answers. What are the differences? Be sure to explain why any differences occurred.

To determine

(a)

Inventory costing methods:

FIFO, LIFO and average cost method, are those method which used for calculation of closing inventory and cost of goods sold.

The cost of ending inventory, the cost of goods sold and gross margin using the FIFO.

Answer to Problem 73APSA

Particular	$\text{ FIFO }\left(\text{\$}\right)\text{ 2018}$	$\text{ FIFO }\left(\text{\$}\right)\text{ 2019}$
Cost of goods sold	$9540$	$4490$
Closing inventory value	$3510$	$1820$

Explanation of Solution

The given information for the year $2018$ is as follows:

Total available units are:

$\text{Opening inventory}=200\text{ units @ \$9 each}$

$\begin{array}{c}\text{Purchases}=300\text{ units @ \$11 each}\\ \text{Purchases}=500\text{ units @ \$12 each}\\ \text{Purchases}=150\text{ units @ \$13 each}\end{array}$

$\text{Total Purchased units = 950}$

$\begin{array}{c}\text{Total available quantity = 200}+9\text{50}\\ \text{= 1150 units}\end{array}$

$\begin{array}{c}\text{Sales}=320+550\text{ units}\\ \text{=870 units}\end{array}$

$\begin{array}{c}\text{Closing inventory }=\text{Beginning inventory + Purchase}-\text{Sales}\\ \text{=200}+950-870\\ =280\text{ units}\end{array}$

The given information for the year $2019$ is as follows:

Total available units are:

$\begin{array}{c}\text{Opening inventory}=130\text{ units @ \$12 each}\\ \text{=}150\text{ units @ \$13 each}\end{array}$

$\text{Purchases}=200\text{ units @ \$14 each}$

$\text{Total Purchased units = 200}$

$\begin{array}{c}\text{Total available quantity = 280}+\text{200}\\ \text{= 480 units}\end{array}$

$\begin{array}{c}\text{Sales}=200+150\text{ units}\\ =\text{350 units}\end{array}$

$\begin{array}{c}\text{Closing inventory }=\text{Beginning inventory + Purchase}-\text{Sales}\\ \text{=280}+200-350\\ =130\text{ units}\end{array}$

Calculation of Closing Inventory as per FIFO Method:

Under this method, which material purchased first, issued first for production. However closing inventory includes last purchased materials in stock. Due to latest purchase in closing inventory, higher value of latest purchase effects cost of goods sold as lower and profit margin will be high.

As in the periodic system, no updated records are available. So, the cost of goods sold will be computed by subtracting the cost of goods available for sale and cost of ending inventory.

The method followed here is FIFO in which the closing inventory of $280$ units will be valued at last price of purchases i.e. $\$12\text{ and \$13}$ in the year $2018$ and $130$ units will be valued at last price of purchases i.e. $\$14$ in the year $2019$ as in this method the sale is made from first purchase which leads to last purchase to be left on the inventory.

In the year $2018$ :

Hence, the closing inventory is $\$3510$ which is comprised of $\text{\$1950}\left(\text{150 units}\times \text{\$13}\right)$ and $\text{\$1560}\left(\text{130 units}\times \text{\$12}\right)$

The cost of goods sold is as follows:

$\begin{array}{c}\text{Cost of Goods Sold}=\left(\text{Cost of goods avilable for sale}-\text{Cost of closing inventory}\right)\\ =\left(\left(\text{Cost of opening inventory}+\text{Cost of purchases}\right)-\text{Cost of closing inventory}\right)\\ =\left(\$13050-\$3510\right)\\ =\$9540\end{array}$

In the year $2019$ :

Hence, the closing inventory is $\text{\$1820}\left(\text{130 units}\times \text{\$14}\right)$.

The cost of goods sold is as follows:

$\begin{array}{c}\text{Cost of Goods Sold}=\left(\text{Cost of goods avilable for sale}-\text{Cost of closing inventory}\right)\\ =\left(\left(\text{Cost of opening inventory}+\text{Cost of purchases}\right)-\text{Cost of closing inventory}\right)\\ =\left(\$6310-\$1820\right)\\ =\$4490\end{array}$

Computation of Gross Margin for the year $2018\text{ and 2019}$ :

Particulars	Amount $\left(\$\right)$ $2018$	Amount $\left(\$\right)$ $2019$
Sales	$21750$ $\left\{\left(320\text{ units}\times \$25\right)+\left(550\text{ units}\times \$25\right)\right\}$	$8750$ $\left\{\left(200\text{ units}\times \$25\right)+\left(150\text{ units}\times \$25\right)\right\}$
Less: Cost of goods sold	$9540$	$4490$
Gross Margin	$12210$	$4260$

To determine

(b)

Inventory costing methods:

FIFO, LIFO and average cost method, are those method which used for calculation of closing inventory and cost of goods sold.

The cost of ending inventory, the cost of goods sold and gross margin using the LIFO.

Answer to Problem 73APSA

Particular	$\text{LIFO }\left(\text{\$}\right)2018$	$\text{LIFO }\left(\text{\$}\right)2019$
Cost of goods sold	$9930$	$4500$
Closing inventory value	$3120$	$1420$

Explanation of Solution

The given information for the year $2018$ is as follows:

Total available units are:

$\text{Opening inventory}=200\text{ units @ \$9 each}$

$\begin{array}{c}\text{Purchases}=300\text{ units @ \$11 each}\\ \text{Purchases}=500\text{ units @ \$12 each}\\ \text{Purchases}=150\text{ units @ \$13 each}\end{array}$

$\text{Total Purchased units = 950}$

$\begin{array}{c}\text{Total available quantity = 200}+9\text{50}\\ \text{= 1150 units}\end{array}$

$\begin{array}{c}\text{Sales}=320+550\text{ units}\\ \text{=870 units}\end{array}$

$\begin{array}{c}\text{Closing inventory }=\text{Beginning inventory + Purchase}-\text{Sales}\\ \text{=200}+950-870\\ =280\text{ units}\end{array}$

The given information for the year $2019$ is as follows:

Total available units are:

$\begin{array}{c}\text{Opening inventory}=130\text{ units @ \$9 each}\\ \text{=}150\text{ units @ \$13 each}\end{array}$

$\text{Purchases}=200\text{ units @ \$14 each}$

$\text{Total Purchased units = 200}$

$\begin{array}{c}\text{Total available quantity = 280}+\text{200}\\ \text{= 480 units}\end{array}$

$\begin{array}{c}\text{Sales}=200+150\text{ units}\\ =\text{350 units}\end{array}$

$\begin{array}{c}\text{Closing inventory }=\text{Beginning inventory + Purchase}-\text{Sales}\\ \text{=280}+200-350\\ =130\text{ units}\end{array}$

Calculation of closing inventory as per LIFO Method:

Under this method, which material purchased last, issued first for production. However closing inventory includes earliest purchased material in stock. Due to earliest purchase material in stock, lower value of earliest purchased effects cost of goods sold as high and profit margin will be lower.

As in the periodic system, no updated records are available. So, the cost of goods sold will be computed by subtracting the cost of goods available for sale and cost of ending inventory.

The method followed here is LIFO in which the closing inventory of $280$ units will be valued at first price of purchases i.e. $\$9\text{ and \$13}$ in the year $2018$ and $130$ units will be valued at first price of purchases i.e. $\$9\text{ and \$13}$ in the year $2019$ as in this method the sale is made from last purchase which leads to first purchase to be left on the inventory.

In the year $2018$ :

Hence, the closing inventory is $\$3120$ which is comprised of $\text{\$1170}\left(\text{130 units @ \$9}\right)$ and $\text{\$1950}\left(\text{150 units @ \$13}\right)$

The cost of goods sold is as follows:

$\begin{array}{c}\text{Cost of Goods Sold}=\left(\text{Cost of goods avilable for sale}-\text{Cost of closing inventory}\right)\\ =\left(\left(\text{Cost of opening inventory}+\text{Cost of purchases}\right)-\text{Cost of closing inventory}\right)\\ =\left(\$13050-\$3120\right)\\ =\$9930\end{array}$

In the year $2019$ :

Hence, the closing inventory is $\$1420$ which is comprised of $\text{\$720}\left(\text{80 units}\times \text{\$9}\right)$ and $\text{\$700}\left(\text{50 units @ \$14}\right)$

The cost of goods sold is as follows:

$\begin{array}{c}\text{Cost of Goods Sold}=\left(\text{Cost of goods avilable for sale}-\text{Cost of closing inventory}\right)\\ =\left(\left(\text{Cost of opening inventory}+\text{Cost of purchases}\right)-\text{Cost of closing inventory}\right)\\ =\left(\$3120-\$1420\right)\\ =\$4500\end{array}$

Computation of Gross Margin for the year $2018\text{ and 2019}$ :

Particulars	Amount $\left(\$\right)$ $2018$	Amount $\left(\$\right)$ $2019$
Sales	$21750$ $\left\{\left(320\text{ units}\times \$25\right)+\left(550\text{ units}\times \$25\right)\right\}$	$8750$ $\left\{\left(200\text{ units}\times \$25\right)+\left(150\text{ units}\times \$25\right)\right\}$
Less: Cost of goods sold	$9930$	$4500$
Gross Margin	$11820$	$4250$

To determine

(c)

Inventory costing methods:

FIFO, LIFO and average cost method, are those method which used for calculation of closing inventory and cost of goods sold.

The cost of ending inventory, the cost of goods sold and gross margin using the average cost method.

Answer to Problem 73APSA

Particular	$\text{Average cost }\left(\text{\$}\right)2018$	$\text{Average cost }\left(\text{\$}\right)2019$
Cost of goods sold	$9875$	$4358$
Closing inventory value	$3178$	$1619$

Explanation of Solution

The given information for the year $2018$ is as follows:

Total available units are:

$\text{Opening inventory}=200\text{ units @ \$9 each}$

$\begin{array}{c}\text{Purchases}=300\text{ units @ \$11 each}\\ \text{Purchases}=500\text{ units @ \$12 each}\\ \text{Purchases}=150\text{ units @ \$13 each}\end{array}$

$\text{Total Purchased units = 950}$

$\begin{array}{c}\text{Total available quantity = 200}+9\text{50}\\ \text{= 1150 units}\end{array}$

$\begin{array}{c}\text{Sales}=320+550\text{ units}\\ \text{=870 units}\end{array}$

$\begin{array}{c}\text{Closing inventory }=\text{Beginning inventory + Purchase}-\text{Sales}\\ \text{=200}+950-870\\ =280\text{ units}\end{array}$

The given information for the year $2019$ is as follows:

Total available units are:

$\text{Opening inventory}=280\text{ units @ \$11}\text{.35 each}$

$\text{Purchases}=200\text{ units @ \$14 each}$

$\text{Total Purchased units = 200}$

$\begin{array}{c}\text{Total available quantity = 280}+\text{200}\\ \text{= 480 units}\end{array}$

$\begin{array}{c}\text{Sales}=200+150\text{ units}\\ =\text{350 units}\end{array}$

$\begin{array}{c}\text{Closing inventory }=\text{Beginning inventory + Purchase}-\text{Sales}\\ \text{=280}+200-350\\ =130\text{ units}\end{array}$

Calculation of closing inventory as per weighted average method:

Under this method, average cost per unit of inventory is calculated and closing inventory value is to be calculated on that basis. Average cost of inventory is changed on purchase high or low. However we follow indirect method of average cost to calculate closing inventory.
As in the periodic system, no updated records are available. So, the cost of goods sold will be computed by subtracting the cost of goods available for sale and cost of ending inventory.

The method followed here is average cost method in which the closing inventory of $280$ units will be valued at average price of purchases i.e. $\$11.35$ in the year $2018$ and $130$ units will be valued at average price of purchases i.e. $\$12.45$ in the year $2019$.

In the year $2018$ :

$\begin{array}{c}\text{Weighted average cost per unit}=\text{Cost of Goods available for sale}÷\text{Units available for sale}\\ \text{=}\left\{\left(\text{200 units}\times \$9\right)+\left(\text{300 units}\times \$11\right)+\left(\text{500 units}\times \$12\right)+\left(\text{150 units}\times \$13\right)\right\}÷1150\\ =\left(\$1800+\$3300+\$6000+1950\right)÷1150\\ =\$11.35\end{array}$

Hence, the closing inventory is $\$3178\left(\text{280 units @ \$11}\text{.35}\right)$

The cost of goods sold is as follows:

$\begin{array}{c}\text{Cost of Goods Sold}=\text{Units sold}\times \text{Average cost}\\ =870\text{ units}\times \$11.35\\ =\$9875\end{array}$

In the year $2019$ :

$\begin{array}{c}\text{Weighted average cost per unit}=\text{Cost of Goods available for sale}÷\text{Units available for sale}\\ \text{=}\left\{\left(\text{280 units}\times \$11.35\right)+\left(\text{200 units}\times \$14\right)\right\}÷480\\ =\left(\$3178+\$2800\right)÷480\\ =\$12.45\end{array}$

Hence, the closing inventory is $\text{\$1619}\left(\text{130 units @ \$12}\text{.45}\right)$

The cost of goods sold is as follows:

$\begin{array}{c}\text{Cost of Goods Sold}=\text{Units sold}\times \text{Average cost}\\ =350\text{ units}\times \$12.45\\ =\$4358\end{array}$

As all the three sales are done after purchases some units and beginning inventory. Hence, there will requirement of various average cost for computing the cost of goods sold.

Computation of Gross Margin for the year $2018\text{ and 2019}$ :

Particulars	Amount $\left(\$\right)$ $2018$	Amount $\left(\$\right)$ $2019$
Sales	$21750$ $\left\{\left(320\text{ units}\times \$25\right)+\left(550\text{ units}\times \$25\right)\right\}$	$8750$ $\left\{\left(200\text{ units}\times \$25\right)+\left(150\text{ units}\times \$25\right)\right\}$
Less: Cost of goods sold	$9875$	$4358$
Gross Margin	$11875$	$4392$

To determine

(d)

Inventory costing methods:

FIFO, LIFO and average cost method, are those method which used for calculation of closing inventory and cost of goods sold.

The method for determining the lowest amount paid for tax.

Answer to Problem 73APSA

The cost of goods sold of LIFO method is higher in both the years and value of closing inventory is lower than other methods in both the years which mean LIFO method provides lowest tax expenses in all methods.

Explanation of Solution

Comparison of closing inventory and Cost of goods sold as per above three methods:

Particulars	FIFO		LIFO		Average Cost
	$2018$	$2019$	$2018$	$2019$	$2018$	$2019$
Cost of goods sold	$9540$	$4490$	$9930$	$4500$	$9875$	$4358$
Closing inventory value	$3510$	$1820$	$3120$	$1420$	$3178$	$1619$

According the evaluation of the above table, it can be concluded that the lowest tax paid is provided by the LIFO method as the expense of cost of goods sold is highest in both the years which makes the income low and lower closing value of inventory in both the years also makes the income lower. Thus, the LIFO is the required method.

To determine

(e)

Inventory costing methods:

FIFO, LIFO and average cost method, are those method which used for calculation of closing inventory and cost of goods sold.

The method for determining the most realistic amount for inventory.

Answer to Problem 73APSA

FIFO method describes most realistic amount of closing inventory. It is not so high or not so less value.

Explanation of Solution

Comparison of closing inventory and Cost of goods sold as per above three methods:

Particulars	FIFO		LIFO		Average Cost
	$2018$	$2019$	$2018$	$2019$	$2018$	$2019$
Cost of goods sold	$9540$	$4490$	$9930$	$4500$	$9875$	$4358$
Closing inventory value	$3510$	$1820$	$3120$	$1420$	$3178$	$1619$

According the evaluation of the above table, it can be concluded that the most realistic amount for the inventory is getting from the method named FIFO method as it provides a medium value i.e. not very high and not very low to affect the income.

To determine

(f)

Gross profit margin ratio:

The gross margin ratio is a type of profitability ratio which is used to measure the returns and earning after direct expenses and compute the ratio in respect to the sales of the business.

Inventory Turnover ratio:

The ratio which measures the efficiency of the company in managing their inventory by diving the cost of goods sold by the average inventory.

The effect of purchases made later in the year on the gross margin when LIFO and FIFO is employed.

Answer to Problem 73APSA

The effect of purchases when LIFO employed is that due to increase in price the cost of goods sold goes to the highest and closing inventory lowest which gives lower gross margin. On using FIFO, the effect is that the prices earlier lowest and then in later increased which makes the cost of goods sold lower and closing inventory value higher which gives higher gross margin.

Explanation of Solution

Particulars	FIFO		LIFO		Average Cost
	$2018$	$2019$	$2018$	$2019$	$2018$	$2019$
Sales $\left(\text{Units sold}\times \$25\right)$ $\left(1\right)$	$\$21750$	$\$8750$	$\$21750$	$\$8750$	$\$21750$	$\$8750$
Less: Cost of goods sold $\left(2\right)$	$9540$	$4490$	$9930$	$4500$	$9369$	$4138$
Gross Profit $\left(3\right)$	$12210$	$4260$	$11820$	$4250$	$11875$	$4392$
Opening Inventory $\left(4\right)$	$1800$	$3510$	$1800$	$3120$	$1800$	$3178$
Closing Inventory $\left(5\right)$	$3510$	$1820$	$3120$	$1420$	$3178$	$1619$

By analyzing the above table, it can be said that the purchases of later time affects the cost of goods sold and closing inventory valuation as they are increasing. In FIFO method, the purchases of earlier period is used for computing cost of goods sold which results in lower value and the inventory left is of later purchases of high value which results in higher value of closing inventory. This results in higher gross margin.

Likewise, opposite scenario is in LIFO method. The purchases of later with increased prices used for computing cost of goods sold which leads to higher cost of goods sold and the inventory left is of earlier period in which purchases of lower value which leads to lower closing inventory value. This results in lower gross margin.

To determine

(g)

Inventory costing methods:

FIFO, LIFO and average cost method, are those method which used for calculation of closing inventory and cost of goods sold.

The difference of the results in two same answers.

Answer to Problem 73APSA

The reason of difference in two same answers is due to the difference in the method followed in both the answers to record the transactions.

Explanation of Solution

On comparison the answer with that of problem $6-68\text{A}$, it is observed that the difference is due to the method of recording the transaction used in the question is different. In the other problem, the method used is perpetuity system in which proper data is recorded and accounts are updated with every transaction of sale and purchase.

In this problem, the method used is the periodic inventory method in which businesses does not maintain up to date records and transactions of every sale and purchase. This method does not affect the answer of FIFO and LIFO method but affect the average cost method and its reason is its difference in timings.