Chapter 17, Problem 4PB

To determine

Calculate the following ratios measures for 20Y2.

1. 1. Working capital
2. 2. Current ratio
3. 3. Quick ratio
4. 4. Accounts receivable turnover
5. 5. Number of days' sales in receivables
6. 6. Inventory turnover ratio
7. 7. Number of days' sales in inventory
8. 8. Ratio of fixed assets to long-term liabilities
9. 9. Ratio of liabilities to stockholders’ equity
10. 10. Times interest earned ratio
11. 11. Asset turnover ratio
12. 12. Return on total assets
13. 13. Return on stockholders' equity
14. 14. Return on common stockholders' equity
15. 15. Earnings per share on common stock
16. 16. Price earnings ratio
17. 17. Dividends per share of common stock
18. 18. Dividend yield

Explanation of Solution

Financial Ratios: Financial ratios are the metrics used to evaluate the capabilities, profitability, and overall performance of a company.

1. Working capital

$\begin{array}{c}\text{Working capital = Current assets – }\text{}\text{Current liabilities }\\ \text{= \$3,690,000 – \$900,000}\\ \text{= \$2,790,000}\end{array}$

Description:

Working capital is determined as the difference between current assets and current liabilities.

Formula:

$\text{Working capital = Current assets – }\text{}\text{Current liabilities }$

2. Current ratio

$\begin{array}{c}\text{Current ratio}=\frac{\text{Current assets}}{\text{Current}\text{liabilities}}\\ =\frac{\text{\$3,690,000}}{\text{\$900,000}}\\ =4.1\end{array}$

Description:

Current ratio is used to determine the relationship between current assets and current liabilities. The ideal current ratio is 2:1.  Current assets include cash and cash equivalents, short-term investments, net, accounts and notes receivables, net, inventories, and prepaid expenses and other current assets. Current liabilities include short-term obligations and accounts payable.  

Formula:

$\text{Current ratio}=\frac{\text{Current assets}}{\text{Current}\text{liabilities}}$

3. Quick ratio

$\begin{array}{c}\text{Quick ratio }=\frac{\text{Quick assets }}{\text{Current}\text{liabilities}}\\ =\frac{\$2,250,000}{\$900,000}\\ =2.5\end{array}$

Description:

Acid-Test Ratio is the ratio denotes that this ratio is a more rigorous test of solvency than the current ratio. It is determined by dividing quick assets and current liabilities. The acceptable acid-test ratio is 0.90 to 1.00. It is referred as quick ratio. Use the following formula to determine the acid-test ratio:

$\text{Acid Ratio}=\frac{\text{Quick assets}}{\text{Current}\text{liabilities}}$

4. Accounts receivable turnover

$\begin{array}{c}\begin{array}{l}\text{Accounts receivables}\\ \text{ turnover ratio}\end{array}\}=\frac{\text{Net credit sales}}{\text{Average accounts receivables}}\\ =\frac{\$10,000,000}{\$625,000}\\ =16.0\end{array}$

Description:

Accounts receivables turnover ratio is mainly used to evaluate the collection process efficiency. It helps the company to know the number of times the accounts receivable is collected in a particular time period. Main purpose of accounts receivable turnover ratio is to manage the working capital of the company. This ratio is determined by dividing credit sales and sales return.

Formula:

$\begin{array}{l}\text{Accounts receivables}\\ \text{ turnover ratio}\end{array}\}=\frac{\text{Net credit sales}}{\text{Average accounts receivables}}$

Average accounts receivable is determined as follows:

$\begin{array}{c}\begin{array}{l}\text{Average accounts }\\ \text{receivables }\end{array}\}\text{= }\frac{\left(\begin{array}{l}\text{Opening accounts receivables }\\ \text{+ Closing accounts receivables }\end{array}\right)}{2}\\ =\frac{\$740,000+\$510,000}{2}\\ =\$625,000\end{array}$

5. Number of days’ sales in receivables

$\begin{array}{c}\begin{array}{l}\text{Number of days’ sales }\\ \text{in receivable }\end{array}\}=\frac{\text{Average accounts receivable }}{\text{Average daily sales}}\\ =\frac{\$625,000}{27,397.26}\\ =22.8\text{days}\end{array}$

Description:

Number of days’ sales in receivables is used to determine the number of days a particular company takes to collect accounts receivables.

Formula:

$\text{Number of days’ sales in receivable}\text{=}\frac{\text{Average accounts receivable }}{\text{Average daily sales}}$

Average daily sales are determined by dividing sales by 365 days.

$\begin{array}{c}\text{Average daily sales = }\frac{\text{Sales}}{\text{365}\text{days}}\\ =\frac{\$10,000,000}{365\text{days}}\\ =\$27,397.26\end{array}$

6. Inventory turnover ratio

$\begin{array}{c}\text{Inventory turnover ratio }=\frac{\text{Cost of goods sold}}{\text{Average inventory}}\\ =\frac{\$5,350,000}{\$1,070,000}\\ =2.2\text{times}\end{array}$

Description:

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

Formula:

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

Average inventory is determined as below:

 $\begin{array}{c}\text{Average inventory = }\frac{\left(\text{Opening inventory + Closing inventory }\right)}{2}\\ =\frac{\$1,190,000+\$950,000}{2}\\ =\$1,070,000\end{array}$

7.  Number of days sales in inventory ratio

$\begin{array}{c}\begin{array}{l}\text{Number of days’ }\\ \text{sales in inventory }\end{array}\}=\frac{\text{Average inventory }}{\text{Average daily cost of goods sold}}\\ =\frac{\$1,070,000}{\$14,657.53}\\ =73.0\text{days}\end{array}$

Description:

Number of days’ sales in inventory is determined as the number of days a particular company takes to make sales of the inventory available with them.

Formula:

$\text{ Number of days’ sales in invenotry}=\frac{\text{Average inventory }}{\text{Average daily cost of goods sold}}$

Average daily cost of goods sold are determined by dividing cost of goods sold by 365 days. Thus, average daily cost of goods sold are determined as follows:

$\begin{array}{c}\text{Average daily cost of goods sold= }\frac{\text{Cost of goods sold}}{\text{365}\text{days}}\\ =\frac{\$5,350,000}{365\text{days}}\\ =\$14,657.53\end{array}$

8. Ratio of fixed assets to long-term liabilities

$\begin{array}{c}\text{Ratio of fixed assets to long-term liabilities}=\frac{\text{Fixed assets }}{\text{Long-term liabilities }}\\ =\frac{\$3,740,000}{\$1,700,000}\\ =2.2\end{array}$

Description:

Ratio of fixed assets to long-term liabilities is determined by dividing fixed assets and long-term liabilities.

Formula:

$\text{Ratio of fixed assets to long-term liabilities}=\frac{\text{Fixed assets }}{\text{Long-term liabilities }}$

9. Ratio of liabilities to stockholders’ equity

$\begin{array}{c}\begin{array}{l}\text{Ratio of liabilities }\\ \text{to stockholders' equity }\end{array}\}=\frac{\text{Total liabilities}}{\text{Stockholders' equity}}\\ =\frac{\$2,600,000}{\$7,180,000}\\ =0.4\end{array}$

Description:

Ratio of liabilities to stockholders’ equity is determined by dividing liabilities and stockholders’ equity.

Formula:

$\text{ Ratio of liabilities to stockholders' equity}=\frac{\text{Total liabilities}}{\text{Stockholders' equity}}$

10. Times interest earned ratio

$\begin{array}{c}\begin{array}{l}\text{Times-interest-}\\ \text{earned ratio }\end{array}\}=\frac{\text{Income before income tax}+\text{Interest expense}}{\text{Interest expense}}\\ =\frac{\$1,130,000+\$170,000}{\$170,000}\\ =7.6\%\end{array}$

Description:

Times interest earned ratio quantifies the number of times the earnings before interest and taxes can pay the interest expense. First, determine the sum of income before income tax and interest expense. Then, divide the sum by interest expense.

Formula:

$\begin{array}{l}\text{Times-interest-}\\ \text{earned ratio }\end{array}\}=\frac{\text{Income before income tax}+\text{Interest expense}}{\text{Interest expense}}$

11. Asset turnover ratio

$\begin{array}{c}\text{Asset turnover ratio }=\frac{\text{Sales}}{\text{Average total assets}}\\ =\frac{\$10,000,000}{\$9,267,500}\\ =1.1\end{array}$

Description:

Asset turnover ratio is used to determine the asset’s efficiency towards sales.

Formula: $\text{Asset turnover }=\frac{\text{Net}\text{revenue}}{\text{Average total assets}}$

Working notes for average total assets are as follows:

$\begin{array}{c}\text{Average total assets =}\frac{\text{Beginning total assets + Ending total assets }}{2}\\ =\frac{\$9,780,000+\$8,755,000}{2}\\ =\$9,267,500\end{array}$

12. Return on total assets

$\begin{array}{c}\text{Return on total assets}=\frac{\text{Net}\text{income + Interest expense}}{\text{Average total assets}}\\ =\frac{\$900,000+\$170,000}{\$9,267,500}\\ =11.5\%\end{array}$

Description:

Return on assets determines the particular company’s overall earning power. It is determined by dividing sum of net income and interest expense and average total assets.

Formula:

$\text{Rate of return on assets}=\frac{\text{Net}\text{income + Interest expense}}{\text{Average total assets}}$

13. Return on stockholders’ equity

 $\begin{array}{c}\begin{array}{l}\text{Return on }\\ \text{stockholders' equity}\end{array}\}=\frac{\text{Net income }}{\text{Average stockholder’s equity}}\\ =\frac{\$900,000}{\$6,777,500}\\ =13.3\%\end{array}$

Description:

Rate of return on stockholders’ equity is used to determine the relationship between the net income and the average equity that are invested in the company.

Formula: $\text{Rate of return on stockholders' equtiy }=\frac{\text{Net income}}{\text{Average stockholder’s equity}}$

Average stockholders’ equity is determined as follows:

$\begin{array}{c}\text{Average stockholders' equity =}\left(\frac{\begin{array}{l}\text{Beginning stockholders' equity }\\ \text{ + Ending stockholders' equity }\end{array}}{2}\right)\\ =\frac{\$7,180,000+\$6,375,000}{2}\\ =\$6,777,500\end{array}$

14. Return on common stockholders’ equity

 $\begin{array}{c}\begin{array}{l}\text{Return on common }\\ \text{stockholders' equity}\end{array}\}=\frac{\text{Net income – Preferred dividends }}{\text{Average stockholder’s equity}}\\ =\frac{\$900,000–\$45,000}{\$6,277,500}\\ =13.6\%\end{array}$

Description:

Rate of return on stockholders’ equity is used to determine the relationship between the net income and the average common equity that are invested in the company.

Formula: $\text{Rate of return on common stockholders' equtiy }=\frac{\text{Net income – Preferred dividends }}{\text{Average common stockholder’s equity}}$

Average common stockholders’ equity is determined as follows:

$\begin{array}{c}\text{Average stockholders' equity =}\left(\frac{\begin{array}{l}\text{Beginning common stockholders' equity }\\ \text{ + Ending common stockholders' equity }\end{array}}{2}\right)\\ =\frac{\$6,680,000+\$5,875,000}{2}\\ =\$6,277,500\end{array}$

15. Earnings per share on common stock

$\begin{array}{c}\text{Earnings per share=}\left(\frac{\text{Net income }–\text{ Preferreddividends}}{\text{Weighted-average common shares outstanding}}\right)\\ =\frac{\$900,000-\$45,000}{100,000}\\ =\$8.55\end{array}$

Description:

A portion of profit that an individual earns from each share is referred to earnings per share.

Formula:

$\begin{array}{l}\text{Earnings }\\ \text{per share}\end{array}\}=\frac{\text{Net income }-\text{Preferred dividends}}{\text{Weighted average number of common shares outstanding}}$

16. Price earnings ratio

$\begin{array}{c}\text{Price earnings ratio =}\frac{\text{Market price per share}}{\text{Earning per share}}\\ \text{=}\frac{\text{\$119}\text{.70}}{\text{\$8}\text{.55}}\\ \text{=14}\text{.0 times}\end{array}$

Description:

Price/earnings ratio is used to determine the profitability of a company. This ratio is abbreviated as P/E.

Formula:

$\text{Price/earnings ratio}=\frac{\text{Market price per share of common stock}}{\text{Earnings per share}}$

17. Dividend per share of common stock

$\begin{array}{c}\begin{array}{l}\text{Dividend per }\\ \text{share of common stock}\end{array}\}=\frac{\text{Dividend per Common stock}}{\text{Shares of common stock}}\times 100\\ =\frac{\$50,000}{100,000\text{shares}}\\ =\$0.50\end{array}$

Description:

Dividend per share of commons stock is determined by dividing dividend per common stock and shares of common stock. 

Formula:

$\begin{array}{l}\text{Dividend per }\\ \text{share of common stock}\end{array}\}=\frac{\text{Dividend per Common stock}}{\text{Shares of common stock}}\times 100$

18. Dividend yield ratio

$\begin{array}{c}\text{Dividend yield }=\frac{\text{Annual dividend per Share}}{\text{Market price per Share}}\times 100\\ =\frac{\$0.50}{\$119.70}\\ =0.4\%\end{array}$

Description:

Dividend yield ratio is determined to evaluate the relationship between the annual dividend per share and the market price per share.  

Formula:

$\text{Dividend yield }=\frac{\text{Annual dividend per Share}}{\text{Market price per Share}}\times 100$

Conclusion

Thus, summary table of determined ratios are below:

S.No	Particulars	Ratios
1.	Working capital	$2,790,000
2.	Current ratio	4.1
3.	Acid test ratio	2.5
4.	Accounts receivable turnover ratio	16.0
5.	Number of days’ sales in receivables	22.8
6.	Inventory turnover ratio	5.0
7.	Number of days sales in inventory	73.0
8.	Ratio of fixed assets to  long-term liabilities	2.2
9.	Ratio of liabilities to stockholders’ equity	0.4
10.	Times interest earned ratio	7.6
11.	Asset turnover ratio	1.1
12.	Return on total assets	11.5%
13.	Return on stockholders’ equity	13.3%
14.	Return on common stockholders’ equity	13.6%
15.	Earnings per share	$8.55
16.	Price earnings ratio	14.0
17.	Dividend  per share of common stock	$0.50
18.	Dividend yield	0.4%