Chapter 13, Problem 23AP

To determine

Compute the ratios for Year 4 and Year 3 for Company K.

Answer to Problem 23AP

Compute ratios of Company K for Year 4 and Year 3:

Ratios and Formula	Year 4	Year 3
a. Net margin: $\frac{\text{Net income}}{\text{Net sales}}$	$\begin{array}{l}=\frac{\$72,000}{\$420,000}\\ =17.14\%\end{array}$	$\begin{array}{l}=\frac{\$54,000}{\$350,000}\\ =15.42\%\end{array}$
b. Return on investment: $\frac{\text{Net income }}{\text{Average total assets}}$	$\begin{array}{l}=\frac{\$72,000}{\$512,000\left(1\right)}\\ =14.06\%\end{array}$	$\begin{array}{l}=\frac{\$54,000}{\$488,000}\\ =11.07\%\end{array}$
c. Return on equity: $\frac{\text{Net income }}{\left[\begin{array}{l}\text{Average stockholders'}\\ \text{ equity}\end{array}\right]}$	$\begin{array}{l}=\frac{\$72,000}{\$253,000\left(2\right)}\\ =28.46\%\end{array}$	$\begin{array}{l}=\frac{\$54,000}{\$216,000}\\ =25\%\end{array}$
d. Earnings per share: $\frac{\text{Net income}}{\left[\begin{array}{l}\text{Average common }\\ \text{shares outstanding}\end{array}\right]}$	$\begin{array}{l}=\frac{\$72,000}{100,000\text{ shares}}\\ =\$0.72\text{ per share}\end{array}$	$\begin{array}{l}=\frac{\$54,000}{100,000\text{ shares}}\\ =\$0.54\text{ per share}\end{array}$
e. Price-earnings ratio: $\frac{\text{Market price per share}}{\text{ Earnings per share}\left(\text{d}\text{.}\right)}$	$\begin{array}{l}=\frac{\$9.54\left(\text{Given}\right)}{\$0.72}\\ =13.25\text{ times}\end{array}$	$\begin{array}{l}=\frac{\$11.88\left(\text{Given}\right)}{\$0.54}\\ =22\text{ times}\end{array}$
f. Book value per share of common stock: $\frac{\left[\begin{array}{l}\text{Stockholders' }\\ \text{equity}\end{array}\right]-\left[\begin{array}{l}\text{Preferred }\\ \text{stock}\end{array}\right]}{\text{Outstanding common shares}}$	$\begin{array}{l}=\frac{\$290,000-\$0}{100,000\text{ shares}}\\ =\$2.90\text{ per share}\end{array}$	$\begin{array}{l}=\frac{\$216,000-\$0}{100,000\text{ shares}}\\ =\$2.16\text{ per share}\end{array}$
g. Times interest earned: $\frac{\left[\begin{array}{l}\text{Earnings before interest}\\ \text{ and tax expense}\end{array}\right]}{\text{Interest expense}}$	$\begin{array}{l}=\frac{\$120,000\left(3\right)}{\$6,000}\\ =20.00\text{ times}\end{array}$	$\begin{array}{l}=\frac{\$96,000\left(4\right)}{\$6,000}\\ =16.00\text{ times}\end{array}$
h. Working Capital: $\left(\begin{array}{l}\text{Current }\\ \text{Assets}\end{array}\right)-\left(\begin{array}{l}\text{Current }\\ \text{Liabilities}\end{array}\right)$	$\begin{array}{l}=\$286,000-\$114,000\\ =\$172,000\end{array}$	$\begin{array}{l}=\$278,000-\$138,000\\ =\$140,000\end{array}$
i. Current ratio: $\frac{\text{Current Assets}}{\text{Current Liabilities}}$	$\begin{array}{l}=\frac{\$286,000}{\$114,000}\\ =2.50:1\end{array}$	$\begin{array}{l}=\frac{\$278,000}{\$138,000}\\ =2.01:1\end{array}$
j. Quick ratio: $\frac{\text{Quick Assets}}{\text{Current Liabilities}}$	$\begin{array}{l}=\frac{\$80,000}{\$114,000}\\ =0.70:1\end{array}$	$\begin{array}{l}=\frac{\$82,000}{\$138,000}\\ =0.59:1\end{array}$
k. Receivables turnover: $\frac{\text{}\text{Net credit sales}}{\left(\begin{array}{l}\text{Average accounts }\\ \text{receivables}\end{array}\right)}$	$\begin{array}{l}=\frac{\$420,000}{\$67,000\left(5\right)}\\ =6.27\text{ times}\end{array}$	$\begin{array}{l}=\frac{\$350,000}{\$64,000}\\ =5.47\text{ times}\end{array}$
l. Inventory turnover: $\frac{\text{Cost of goods sold}}{\text{Average inventory}}$	$\begin{array}{l}=\frac{\$252,000}{\$196,000\left(6\right)}\\ =1.28\text{ times}\end{array}$	$\begin{array}{l}=\frac{\$206,000}{\$192,000}\\ =1.07\text{ times}\end{array}$
m. Debt to equity ratio: $\frac{\text{Total liabilities }}{\left(\begin{array}{l}\text{Total stockholders' }\\ \text{equity}\end{array}\right)}$	$\begin{array}{l}=\frac{\$246,000}{\$290,000}\\ =0.85:1\end{array}$	$\begin{array}{l}=\frac{\$272,000}{\$216,000}\\ =1.26:1\end{array}$
n. Debt to assets ratio: $\frac{\text{Total liabilities }}{\text{Total assets}}$	$\begin{array}{l}=\frac{\$246,000}{\$536,000}\\ =45.89\%\end{array}$	$\begin{array}{l}=\frac{\$272,000}{\$488,000}\\ =55.73\%\end{array}$

Table (1)

Explanation of Solution

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

1. a. Net profit margin: It is one of the profitability ratios. Profit margin ratio is used to measure the percentage of net income that is being generated per dollar of revenue or sales.

$\text{Net margin}=\frac{\text{Net income}}{\text{Net sales}}$

1. b. Return on investments (assets): Return on investments (assets) is the financial ratio which determines the amount of net income earned by the business with the use of total assets owned by it. It indicates the magnitude of the company’s earnings with relative to its total assets. Return on investment is calculated as follows:

$\text{Return on investments}=\frac{\text{Net income }}{\text{Average total assets}}$

1. c. Return on equity: It is a profitability ratio that measures the profit generating ability of the company from the invested money of the shareholders. The formula to calculate the return on equity is as follows:

$\text{Return on equity}=\frac{\text{Net income}}{\text{Average stockholders' equity}}\times 100$

1. d. Earnings per Share: Earnings per share help to measure the profitability of a company. Earnings per share are the amount of profit that is allocated to each share of outstanding stock.

$\text{Earnings per share}=\frac{\text{Net earnings available for common stock}}{\text{Average number of outstanding common shares}}$

1. e. Price/Earnings Ratio: The price/earnings ratio shows the market value of the amount invested to earn $1 by a company. It is major tool used by investors for making decisions related to the investment in a company.

$\text{Price/Earnings Ratio}\text{=}\frac{\text{Market Price per Share }}{\text{Earnings per Share}}$

1. f. Book value per share of common stock: This ratio is a measure of a share of common stock that is used to determine the value of per share based on the equity available to the common stockholders. This ratio is calculated by using the formula:

$\begin{array}{l}\text{Book value per share }\\ \text{of common stock}\end{array}\}\text{=}\frac{\text{Stockholders' equity}-\text{Preferred stock }}{\text{Outstanding common shares}}$

1. g. Times interest earned: Number of times interest is earned 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.

$\text{Times interest earned}=\frac{\text{Earnings before interest and taxes expense}}{\text{ Interest expense }}$

1. h. Working capital: Working capital refers to the excess amount of current assets over its current liabilities of a business. It measures the excess funds that are required for the companies to carry out their day to day operations, excluding any new funds that have been invested during the year. Working capital is calculated by using the formula:

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

1. i. Current ratio: Current ratio is one of the liquidity ratios, which measures the capacity of the company to meet its short-term obligations using its current assets. Current ratio is calculated by using the formula:

$\text{Current ratio}=\frac{\text{Current Assets}}{\text{Current Liabilities}}$

1. j. Quick ratio: It is a ratio used to determine a company’s ability to pay back its current liabilities by liquid assets that are current assets except inventory and prepaid expenses.

$\text{Quick ratio}=\frac{\text{Quick Assets}}{\text{Current Liabilities}}$

1. k. Account Receivables turnover ratio: Account 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. This ratio is determined by dividing credit sales and sales return.

$\text{Receivables turnover}=\frac{\text{}\text{Net credit sales}}{\text{Average accounts receivables}}$

1. l. Inventory Turnover Ratio: This ratio is a financial metric used by a company to quantify the number of times inventory is used or sold during the accounting period. It is calculated by using the formula:

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

1. m. Debt–to-equity ratio: The debt-to-equity ratio indicates that the company’s debt as a proportion of its stockholders’ equity. The debt-to-equity ratio is calculated using the formula:

$\text{Debt-to-equity ratio}=\frac{\text{Total liabilities}}{\text{Total stockholders' equity}}$

1. n. Debt to assets ratio: The debt to asset ratio shows the relationship between total asset and the total liability of the company. Debt ratio reflects the financial strategy of the company. It is used to measure the percentage of company’s assets that are financed by long term debts.  Debt to assets ratio is calculated by using the formula:

   $\text{Debt-to-assets ratio}=\frac{\text{Total Liabilities}}{\text{Total Assets }}$

Note:

1. 1. Quick assets include cash, marketable securities and accounts receivable.
2. 2. Since, the beginning values of receivable, inventory, assets and stockholders’ equity for Year 3 is not given. So, the total amount of receivable, inventory, assets and stockholders’ equity for Year 3 is assumed as average total assets and average total stockholders’ equity.

Working Note:

Determine the amount of average total assets for Year 4.

$\begin{array}{c}\text{Average total assets =}\frac{\left(\begin{array}{l}\text{Ending }\\ \text{total assets}\end{array}\right)+\left(\begin{array}{l}\text{Beginning }\\ \text{total assets}\end{array}\right)}{2}\\ =\frac{\$536,000+\$488,000}{2}\\ =\frac{\$1,024,000}{2}\\ =\$512,000\end{array}$ (1)

Determine the amount of average total stockholders’ equity for Year 4.

$\begin{array}{c}\begin{array}{l}\text{Average total }\\ \text{stockholders' equity }\end{array}\}\text{=}\frac{\left(\begin{array}{l}\text{Ending total }\\ \text{stockholders' equity}\end{array}\right)+\left(\begin{array}{l}\text{Beginning total }\\ \text{stockholders' equity}\end{array}\right)}{2}\\ =\frac{\$290,00+\$216,000}{2}\\ =\frac{\$506,000}{2}\\ =\$253,000\end{array}$ (2)

Determine the amount of earnings before interest and expenses for Year 4.

$\begin{array}{c}\begin{array}{l}\text{Earnings before income }\\ \text{tax and interest}\end{array}\}=\left(\begin{array}{l}\text{Net }\\ \text{Income}\end{array}\right)+\left(\begin{array}{l}\text{Interest}\\ \text{ expense}\end{array}\right)+\left(\begin{array}{l}\text{Tax}\\ \text{ expense}\end{array}\right)\\ =\$72,000+\$6,000+\$42,000\\ =\$120,000\end{array}$ (3)

Determine the amount of earnings before interest and expenses for Year 3.

$\begin{array}{c}\begin{array}{l}\text{Earnings before income }\\ \text{tax and interest}\end{array}\}=\left(\begin{array}{l}\text{Net }\\ \text{Income}\end{array}\right)+\left(\begin{array}{l}\text{Interest}\\ \text{ expense}\end{array}\right)+\left(\begin{array}{l}\text{Tax}\\ \text{ expense}\end{array}\right)\\ =\$54,000+\$6,000+\$36,000\\ =\$96,000\end{array}$ (4)

Determine the amount of average accounts receivable for Year 4.

$\begin{array}{c}\begin{array}{l}\text{Average accounts}\\ \text{ receivable}\end{array}\}=\frac{\left(\begin{array}{l}\text{Ending Net }\\ \text{Receivables}\end{array}\right)+\left(\begin{array}{l}\text{Beginning Net }\\ \text{Receivables}\end{array}\right)}{2}\\ =\frac{\$70,000+\$64,000}{2}\\ =\frac{\$134,000}{2}\\ =\$67,000\end{array}$

…… (5)

Determine the amount of average inventory for Year 4.

$\begin{array}{c}\text{Average inventory}=\frac{\left(\begin{array}{l}\text{Ending }\\ \text{Inventory}\end{array}\right)+\left(\begin{array}{l}\text{Beginning}\\ \text{ Inventory}\end{array}\right)}{2}\\ =\frac{\$200,000+\$192,000}{2}\\ =\frac{\$392,000}{2}\\ =\$196,000\end{array}$

…… (6)