Chapter 4, Problem 4.12P

Calculating activity and profitability ratios

• LO4–10

Financial statements for Askew Industries for 2018 are shown below (in thousands):

2018 Income Statement

Sales	$9,000
Cost of goods sold	(6,300)
Gross profit	2,700
Operating expenses	(2,000)
Interest expense	(200)
Tax expense	(200)
Net income	$ 300

Comparative Balance Sheets

		Dec. 31
	2018	2017
Assets
Cash	$ 600	$ 500
Accounts receivable	600	400
Inventory	800	600
Property, plant, and equipment (net)	2,000	2,100
	$4,000	$3,600
Liabilities and Shareholders’ Equity
Current liabilities	$1,100	$ 850
Bonds payable	1,400	1,400
Paid-in capital	600	600
Retained earnings	900	750
	$4,000	$3,600

Required:

Calculate the following ratios for 2018.

1. 1. Inventory turnover ratio
2. 2. Average days in inventory
3. 3. Receivables turnover ratio
4. 4. Average collection period
5. 5. Asset turnover ratio
6. 6. Profit margin on sales
7. 7. Return on assets
8. 8. Return on shareholders’ equity
9. 9. Equity multiplier
10. 10. Return on shareholders’ equity (using the DuPont framework)

To determine

Activity ratios:

It measures the capacity of a company to use its asset, liability and capital accounts to generate revenue in the form of cash.

Profitability ratios:

It measures the companies efficiency of operations and performance that generates profit

 For the company

To calculate: Inventory turnover ratio of A Incorporation for the year 2018.

Explanation of Solution

Calculate the inventory turnover ratio of A Incorporation for the year 2018

$\begin{array}{c}\text{Inventory}\text{turnover}\text{ratio=}\frac{\text{cost}\text{of}\text{goods}\text{sold}}{\text{Average}\text{inventory(1)}}\\ \text{=}\frac{\text{\$6,300}}{\$700}\\ \text{=9}\text{.0 Times}\end{array}$

Working note:

$\begin{array}{c}\text{Average}\text{inventory=}\frac{\text{Ending}\text{inventory+Beginning}\text{inventory}}{\text{2}}\\ \text{=}\frac{\text{\$800+\$600}}{\text{2}}\\ \text{=\$700}\text{.}\end{array}$ (1)

Explanation:

Inventory turnover ratio is used to determine the number of times inventory used (or) sold during the particular accounting period.

Conclusion

Hence, the inventory turnover ratio of A Incorporation is 9.0 Times for the year 2018.

To determine

To calculate: Average days in inventory of A Incorporation for the year 2018.

Explanation of Solution

Calculate the average days in inventory of A Incorporation for the year 2018

$\begin{array}{c}\text{Average}\text{days}\text{in}\text{inventory=365}\frac{\text{Average}\text{inventory(2)}}{\text{cost}\text{ofgoods}\text{sold}}\\ \text{=365}\frac{\text{\$700}}{\text{\$6300}}\\ \text{=40}\text{.56 Days}\text{.}\end{array}$

Working note:

$$ $\begin{array}{c}\text{Average}\text{inventory=}\frac{\text{Ending}\text{inventory+Beginning}\text{inventory}}{\text{2}}\\ \text{=}\frac{\text{\$800+\$600}}{\text{2}}\\ \text{=\$700}\text{.}\end{array}$ (2)

On the Average A Incorporation takes 40 days to convert inventory into sales in the operation cycle.

Conclusion

Hence, the average days in inventory for A Incorporation for the year 2018 is 40.56 Days

To determine

To calculate: Receivables turnover ratio of A Incorporation for the year 2018

Explanation of Solution

Calculate the receivables turnover ratio of A Incorporation for the year ended 2018

$\begin{array}{c}\text{Receivables}\text{turnover}\text{ratio=}\frac{\text{Sales}}{\text{Average}\text{accounts}\text{receivables(3)}}\\ \text{=}\frac{\text{\$9,000}}{\text{\$500}}\\ \text{=18}\text{Times}\end{array}$

Working note:

$\begin{array}{c}\text{Average}\text{accounts}\text{receivables=}\frac{\left(\begin{array}{l}\text{Ending}\text{accounts}\text{receivables+}\\ \text{Beginning}\text{accounts}\text{receivables}\end{array}\right)}{\text{2}}\\ \text{=}\frac{\text{\$600+\$400}}{\text{2}}\\ \text{=\$500}\end{array}$ (3)

Receivables turnover ratio indicates how quickly a company is able to collect its accounts receivable.

Conclusion

Hence, the Receivables turnover ratio of A Incorporation is 18 Times for the year 2018

To determine

To calculate: Average collection period of A Incorporation for the year 2018

Explanation of Solution

Calculate the Average collection period of A Incorporation for the year 2018

$\begin{array}{c}\text{Average}\text{collection}\text{period=365}\frac{\text{Average}\text{accounts}\text{receivables (4)}}{\text{sales}}\\ \text{=365}\frac{\text{\$500}}{\text{\$9,000}}\\ \text{=20}\text{.28Days}\end{array}$

Working note:

$\begin{array}{c}\text{Average}\text{accounts}\text{receivables=}\frac{\left(\begin{array}{l}\text{Ending}\text{accounts}\text{receivables+}\\ \text{Beginning}\text{accounts}\text{receivables}\end{array}\right)}{\text{2}}\\ \text{=}\frac{\text{\$600+\$400}}{\text{2}}\\ \text{=\$500}\end{array}$ (4)

On the average it takes 20.28 days for A Incorporation to collect receivables from its customers.

Conclusion

Hence the, Average collection period of A Incorporation for the year 2018 is 20.28 Days for the year 2018.

To determine

To calculate: Asset turnover ratio of A Incorporation for the year 2018

Explanation of Solution

Calculate the Asset turnover ratio of A Incorporation for the year 2018

$\begin{array}{c}\text{Asset}\text{turnover}\text{ratio=}\frac{\text{Total}\text{revenues}}{\text{Total}\text{assets(5)}}\\ \text{=}\frac{\text{\$9,000}}{\text{\$3,800}}\\ \text{=2}\text{.37}\end{array}$

Working note:

1. Calculate the total assets:

$\begin{array}{c}\text{Total}\text{assets=}\frac{\left(\begin{array}{l}\text{Assets}\text{at}\text{the}\text{beginning+}\\ \text{Assets}\text{at}\text{the}\text{ending}\end{array}\right)}{\text{2}}\\ \text{=}\frac{\text{\$4,000+\$3,600}}{\text{2}}\\ \text{=\$3,800}\text{.}\end{array}$ (5)

Total assets turnover ratio indicates that A Incorporation has generated $2.37 in sales for every $1.00 of assets.

Conclusion

Hence, the Asset turnover ratio of A Incorporation is $2.37 for the year ended 2018.

To determine

To calculate: Profit margin on sales of A Incorporation for the year ended 2018

Explanation of Solution

Calculate the profit margin on sales of A Incorporation for the year ended 2018

$\begin{array}{c}\text{Profit}\text{margin}\text{on}\text{sales=}\frac{\text{\$Net}\text{Income}}{\text{\$Sales}}\\ =\frac{\$300}{\$9,000}\times 100\\ =3.33\%\end{array}$

Profit margin on sales of A Incorporation has Net income of $0.033 for every $1.00 of Total revenue earned.

Conclusion

Hence, the Profit margin on sales of A Incorporation is 3.33% for the year 2018

To determine

To calculate: Return on assets of A Incorporation for the year ended 2018.

Explanation of Solution

Calculate the Return on assets of A Incorporation for the year ended 2018

$\begin{array}{c}\text{Return}\text{on}\text{assets=}\frac{\text{Net}\text{income}}{\text{Total}\text{assets(6)}}\times 100\\ \text{=}\frac{\text{\$300}}{\text{\$3,800}}\times 100\\ \text{=7}\text{.89\%}\\ \left(\text{Or}\right)\\ \text{Return}\text{on}\text{assets=Profit}\text{margin}\text{on}\text{sales×Assets}\text{turnover}\text{ratio}\\ \text{=3}\text{.33\%×2}\text{.37Times}\\ \text{=7}\text{.89\%}\end{array}$

Working note:

Calculate the total assets

$\begin{array}{c}\text{Total}\text{assets=}\frac{\left(\begin{array}{l}\text{Assets}\text{at}\text{the}\text{beginning+}\\ \text{Assets}\text{at}\text{the}\text{ending}\end{array}\right)}{\text{2}}\\ \text{=}\frac{\text{\$4,000+\$3,600}}{\text{2}}\\ \text{=\$3,800}\text{.}\end{array}$ (6)

 7.89% of profit is earned by A Incorporation in relation to its total assets for the year ended 2018.

Conclusion

Hence, the rate of return of A Incorporation is 7.89% for the year ended 2018.

To determine

To calculate: Return on shareholders’ equity of A Incorporation for the year ended 2018

Explanation of Solution

Calculate the return on shareholders’ equity of A Incorporation for the year ended 2018

$\begin{array}{c}\text{Return}\text{on}\text{ shareholders'}\text{equity=}\frac{\text{Net}\text{Income}}{\text{Total}\text{equity(7)}}\times 100\\ \text{=}\frac{\text{\$300}}{\text{\$925}}\text{×100}\\ \text{=21}\text{.1\%}\end{array}$

Working notes:

1. Calculate the total shareholders’ equity at the beginning and total shareholders’ equity at the ending

Details	year	year
	2018	2017
Paid in capital	$600	$600
Retained earning	$900	$750
Total	$1,500	$1,350

Table (1)

 2.  Calculate the total equity

$\begin{array}{c}\text{Total}\text{equity=}\frac{\left[\left(\begin{array}{l}\text{Total}\text{shareholders'}\text{Equity}\text{at}\text{beginning+}\\ \text{Total}\text{shareholders'}\text{Equity}\text{at}\text{ending}\end{array}\right)\right]}{\text{2}}\\ \text{=}\frac{\text{\$1,500+\$1,350}}{\text{2}}\\ \text{=\$925}\text{.}\end{array}$ (7)

Rate of return on shareholders’ equity reveals the profit that the company generates with the money shareholders’ have invested.

Conclusion

Hence, the rate of return of shareholders’ equity of A Incorporation for the year ended 2018 is 21.1%

To determine

To Calculate: Equity multiplier of A Incorporation for the year 2018

Explanation of Solution

Calculate the Equity multiplier of A Incorporation for the year 2018

$\begin{array}{c}\text{Equity}\text{multiplier=}\frac{\text{Total}\text{assets(8)}}{\text{Shareholders'equity(9)}}\\ \text{=}\frac{\$3,800}{\$1,425}\\ \text{=2}\text{.67}\end{array}$

Working note:

1. Calculate total assets

$\begin{array}{c}\text{Total}\text{assets=}\frac{\text{Beginning}\text{assets+Ending}\text{assets}}{\text{2}}\\ \text{=}\frac{\text{\$4,000+\$3,600}}{\text{2}}\\ \text{=\$3,800}\text{.}\end{array}$ (8)

2. Calculate the total shareholders’ equity at the beginning and total shareholders’ equity at the ending

Details	year	year
	2018	2017
Paid in capital	$600	$600
Retained earning	$900	$750
Total	$1,500	$1,350

Table (2)

3. Calculate total shareholders’ equity

$\begin{array}{c}\text{Total}\text{shareholders'}\text{equity=}\frac{\left(\begin{array}{l}\text{Shareholders'}\text{equity}\text{at}\text{the}\text{beginning+}\\ \text{Shareholders'}\text{equity}\text{at}\text{the}\text{ending}\end{array}\right)}{\text{2}}\\ \text{=}\frac{\text{\$1,500+\$1,350}}{\text{2}}\\ \text{=\$1,425}\text{.}\end{array}$ (9)

Equity multiplier is the financial leverage ratio that measures the total asset of the company to its total shareholders’ equity. If the ratio is higher than the company uses more of debt financing than equity.

Conclusion

Hence, the equity multiplier of A Incorporation is 2.67 for the year ended 2018.

To determine

To Calculate: Return on shareholders’ equity (using the DuPont framework) for the year

2018.

Explanation of Solution

Calculate the Return on shareholders’ equity (using the DuPont framework) for the

Year 2018

$\begin{array}{c}\left[\begin{array}{l}\text{Return}\text{on}\text{shareholders'equity}\\ \left(\text{Using}\text{DuPont}\text{framework}\right)\end{array}\right]\text{=}\left(\text{Profit}\text{margin}\text{on}\text{sales×Asset}\text{turnover}\text{ratio×Equity}\text{multiplier}\right)\\ \text{=}\left(\text{3}\text{.33\%×2}\text{.37×2}\text{.67}\right)\\ \text{=21}\text{.1\%}\end{array}$

DuPont framework of measuring Return on shareholders’ equity states that

The company’s Return on equity can be measured by the product of three ratios namely;

1. Profit margin on sales

2. Asset turnover ratio

3. Equity multiplier

Conclusion

Hence, the Return on shareholders’ equity of A Incorporation for the year

2018 is 21.1%.