Chapter 6, Problem 6.11E

(a)

To determine

Inventory turnover ratio: This is a financial measure that is used to evaluate as to how many times a company sells or uses its inventory during an accounting period. It is calculated by using the following formula:

$\text{Inventory turnover = }\frac{\text{Cost of goods sold}}{\text{Average inventory}}$

Days’ sales in inventory: Days’ sales in inventory are used to determine number of days a particular company takes to make sales of the inventory available with them.

$\text{Days' sales in inventory}=\frac{\text{Days in accounting period}}{\text{Inventory turnover}}$

Gross profit rate is the financial ratio that evaluates the money left over out of the total revenues after deducting the cost of goods sold. Thus, it shows the relationship between the gross profit and net sales. It is calculated by using the following formula:

$\text{Gross profit rate}=\frac{\text{Gross profit}}{\text{Net sales}}\times 100$

To Calculate: The inventory turnover for 2015, 2016, and 2017 of Company P.

Explanation of Solution

Calculate the inventory turnover of Company P for 2015.

Cost of goods sold = $18,038

Average inventory = $2,108 (1)

$\begin{array}{c}\text{Inventory}\text{turnover for 2015}\}=\frac{\text{Cost}\text{of}\text{goods}\text{sold}}{\text{Average inventory}}\\ =\frac{\$18,038}{\$2,108}\\ =8.56\text{times}\end{array}$

Calculate the inventory turnover of Company P for 2016.

Cost of goods sold = $20,351

Average inventory = $2,406 (2)

$\begin{array}{c}\text{Inventory}\text{turnover for 2016}\}=\frac{\text{Cost}\text{of}\text{goods}\text{sold}}{\text{Average inventory}}\\ =\frac{\$20,351}{\$2,406}\\ =8.46\text{times}\end{array}$

Calculate the inventory turnover of Company P for 2017.

Cost of goods sold = $20,099

Average inventory = $2,570 (3)

$\begin{array}{c}\text{Inventory}\text{turnover for 2017}\}=\frac{\text{Cost}\text{of}\text{goods}\text{sold}}{\text{Average inventory}}\\ =\frac{\$20,099}{\$2,570}\\ =7.82\text{times}\end{array}$

Working Notes:

Calculate the average inventory for 2015.

Beginning inventory = $1,926

Ending inventory = $2,290

$\begin{array}{c}\text{Average Inventory}=\frac{\text{Beginning Inventory}+\text{Ending Inventory}}{2}\\ =\frac{\$1,926+\$2,290}{2}\\ =\frac{\$4,216}{2}\\ =\$2,108\end{array}$ (1)

Calculate the average inventory for 2016.

Beginning inventory = $2,290

Ending inventory = $2,522

$\begin{array}{c}\text{Average Inventory}=\frac{\text{Beginning Inventory}+\text{Ending Inventory}}{2}\\ =\frac{\$2,290+\$2,522}{2}\\ =\frac{\$4,812}{2}\\ =\$2,406\end{array}$ (2)

Calculate the average inventory for 2017.

Beginning inventory = $2,522

Ending inventory = $2,618

$\begin{array}{c}\text{Average Inventory}=\frac{\text{Beginning Inventory}+\text{Ending Inventory}}{2}\\ =\frac{\$2,522+\$2,618}{2}\\ =\frac{\$5,140}{2}\\ =\$2,570\end{array}$ (3)

Conclusion

Therefore, the inventory turnover of Company P for 2015, 2016, and 2017 are 8.56 times, 8.54 times, and 7.82 times respectively.

 (b)

To determine

To Calculate: The days in inventory of Company P for 2015, 2016, and 2017.

Explanation of Solution

Calculate days in inventory of Company P for 2015.

Total number of days = 365

Inventory turnover, 2015 = 8.56 times (a)

$\begin{array}{c}\text{Days}\text{in}\text{inventory}\text{for 2015}\}=\frac{\text{Total}\text{number}\text{of}\text{days}}{\text{Inventory}\text{turnover}}\\ =\frac{365\text{days}}{8.56\text{times}}\\ =42.64\text{Days}\end{array}$

Calculate days in inventory of Company P for 2016.

Total number of days = 365

Inventory turnover, 2015 = 8.46 times (a)

$\begin{array}{c}\text{Days}\text{in}\text{inventory for 2016}\}\text{=}\frac{\text{Total}\text{number}\text{of}\text{days}}{\text{Inventory}\text{turnover}}\\ =\frac{365\text{days}}{8.46\text{times}}\\ =43.14\text{Days}\end{array}$

Calculate days in inventory of Company P for 2017.

Total number of days = 365

Inventory turnover, 2015 = 7.82 times (a)

$\begin{array}{c}\text{Days}\text{in}\text{inventory for 2017}\}\text{=}\frac{\text{Total}\text{number}\text{of}\text{days}}{\text{Inventory}\text{turnover}}\\ =\frac{365\text{days}}{7.82\text{times}}\\ =46.67\text{Days}\end{array}$

Conclusion

Therefore, the days in inventory of Company P for 2015, 2016, and 2017 are 42.64 days, 43.14 days, and 46.67 days respectively.

(c)

To determine

To Calculate: The gross profit rate of Company P for 2015, 2016, and 2017.

Explanation of Solution

Calculate gross profit rate of Company P for 2015.

Gross profit = $21,436 (4)

Sales revenue = $39,474

$\begin{array}{c}\text{Gross}\text{profit}\text{rate of 2015}\}=\frac{\text{Gross}\text{Profit}}{\text{Sales}\text{revenue}}\times 100\\ =\frac{\$21,436}{\$39,474}\times 100\\ =54.3\%\end{array}$

Calculate gross profit rate of Company P for 2016.

Gross profit = $22,900 (5)

Sales revenue = $43,251

$\begin{array}{c}\text{Gross}\text{profit}\text{rate of 2016}\}=\frac{\text{Gross Profit}}{\text{Sales}\text{revenue}}\\ =\frac{\$22,900}{\$43,251}\\ =52.9\%\end{array}$

Calculate gross profit rate of Company P for 2017.

Gross profit = $23,133 (6)

Sales revenue = $43,232

$\begin{array}{c}\text{Gross}\text{profit}\text{rate of 2017}\}=\frac{\text{Gross profit}}{\text{sales}\text{revenue}}\\ =\frac{\$23,133}{\$43,232}\\ =53.5\%\end{array}$

Working Notes:

Calculate the gross profit for 2015.

Sales revenue = $39,474

Cost of goods sold = $18,038

$\begin{array}{c}\text{Gross}\text{profit of 2015}\}=\text{Sales revenue}-\text{Cost of goods sold}\\ =\$39,474-\$18,038\\ =\$21,436\end{array}$ (4)

Calculate the gross profit for 2016.

Sales revenue = $43,251

Cost of goods sold = $20,351

$\begin{array}{c}\text{Gross}\text{profit of 2016}\}=\text{Sales revenue}-\text{Cost of goods sold}\\ =\$43,251-\$20,351\\ =\$22,900\end{array}$ (5)

Calculate the gross profit for 2017.

Sales revenue = $43,232

Cost of goods sold = $20,099

$\begin{array}{c}\text{Gross}\text{profit of 2017}\}=\text{Sales revenue}-\text{Cost of goods sold}\\ =\$43,232-\$20,099\\ =\$23,133\end{array}$ (6)

Conclusion

Therefore, the gross profit rate of Company P for 2015, 2016, and 2017 are 54.3%, 52.9%, and 53.5% respectively.

(d)

To determine

To Comment: On the above observed trends.

Explanation of Solution

From the above computation, it is clear that the Company P has a decrease in inventory turnover from 2015 to 2017 by 9%. But there is an initial increase in days in inventory by almost 9% over the same time period. Thus, these changes will lead to indicate that it’s better to have a higher inventory turnover with a corresponding lower day in inventory.

This is a positive sign for Company P in running the business.