Chapter 13, Problem 10EYK

1.

To determine

Calculate the profitability ratios: a) return on sales, b) return on common stockholders’ equity for the years 2013 and 2012.

Explanation of Solution

a) Return on sales ratio: The ratio which evaluates the amount of net income earned for every dollar of net sales is referred to as return on sales ratio. Higher ratio indicates highly profitable company.

$\text{Return on sales ratio = }\frac{\text{Net income}}{\text{Net sales}}$

Compute the return on sales ratio for Company F for the year 2013.

Net sales = $980

Net income = $10,000

$\begin{array}{c}\text{Return on sales ratio = }\frac{\text{Net income}}{\text{Net sales}}\\ \text{= }\frac{\text{\$10,000}}{\text{\$980}}\\ \text{= 0}\text{.098 or 9}\text{.8\%}\end{array}$

Hence, return on sales ratio for 2013 is 9.8%.

Compute the return on sales ratio for Company F for the year 2012.

Net sales = $9,500

Net income = $950

$\begin{array}{c}\text{Return on sales ratio = }\frac{\text{Net income}}{\text{Net sales}}\\ \text{= }\frac{\text{\$9,500}}{\text{\$950}}\\ \text{= 0}\text{.10 or 10\%}\end{array}$

Hence, return on sales ratio for 2012 is 10%.

b) Return on common stockholders’ equity ratio: Rate of return on equity ratio is used to determine the relationship between the net income available for the common stockholders’ and the average common equity that is invested in the company.

$\text{Return on Common}\text{Stockholders'}\text{ Equity}\text{=}\frac{\text{Net}\text{Income - preference dividend}}{\text{Average Common}\text{Stockholders'}\text{Equity}}$

Compute the return on common stockholders’ equity for the Company F for the year 2013.

Net income = $980

Average common stockholders’ equity = $2,350 (1)

Preference dividends = $0

$\begin{array}{c}\text{Return on common stockholders' equity}=\frac{\text{Net income}\text{–Preference dividends}}{\text{Average common stockholders' equity}}\times 100\\ =\frac{\$980–\$0}{\$2,350}\times 100\\ =41.7\%\end{array}$

Hence, return on common stockholders’ equity for 2013 is 41.7%.

Compute the return on common stockholders’ equity for the Company F for the year 2012.

Net income = $950

Average common stockholders’ equity = $2,100 (2)

Preference dividends = $0

$\begin{array}{c}\text{Return on common stockholders' equity}=\frac{\text{Net income}\text{–Preference dividends}}{\text{Average common stockholders' equity}}\times 100\\ =\frac{\$950–\$0}{\$2,100}\times 100\\ =45.2\%\end{array}$

Hence, return on common stockholders’ equity for 2012 is 45.2%.

Working notes:

Compute average stockholders’ equity for 2013:

Opening balance of common stockholder’s equity = $2,200

Closing balance of common stockholder’s equity = $2,500

$\begin{array}{c}\text{Average common stockholders’ equity}=\left(\frac{\begin{array}{l}\text{Opening balance of stockholders’ equity }\\ +\text{Closing balance of stockholders’ equity }\end{array}}{2}\right)\\ =\frac{\$2,200+\$2,500}{2}\\ =\frac{\$4,700}{2}\\ =\$2,350\end{array}$ (1)

Compute average stockholders’ equity for 2012:

Opening balance of common stockholder’s equity = $2,000

Closing balance of common stockholder’s equity = $2,200

$\begin{array}{c}\text{Average common stockholders’ equity}=\left(\frac{\begin{array}{l}\text{Opening balance of stockholders’ equity }\\ +\text{Closing balance of stockholders’ equity }\end{array}}{2}\right)\\ =\frac{\$2,000+\$2,200}{2}\\ =\frac{\$4,200}{2}\\ =\$2,100\end{array}$ (2)

2.

To determine

Calculate the liquidity ratios a) current ratio, b) accounts receivable turnover, and c) inventory turnover for the years 2013 and 2012

Explanation of Solution

a) 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. The ideal current ratio is 2:1. The following formula is used to calculate current ratio.

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

Compute current ratio for Company F for the year 2013.

Current assets = $2,200 million

Current liabilities = $3,000 million

$\begin{array}{c}\text{Current ratio=}\frac{\text{Current assets}}{\text{Current}\text{liabilities}}\\ \text{=}\frac{\text{\$2,200 million}}{\$3,000\text{ million}}\\ \text{=}\text{0}\text{.73 times}\end{array}$

Current ratio for 2013 is 0.73 times.

Compute current ratio for Company F for the year 2012.

Current assets = $2,100 million

Current liabilities = $2,900 million

$\begin{array}{c}\text{Current Ratio=}\frac{\text{Current assets}}{\text{Current}\text{liabilities}}\\ \text{=}\frac{\$2,100\text{ million}}{\text{\$2,900 million}}\\ \text{=}\text{0}\text{.72 times}\end{array}$

Current ratio for 2012 is 0.72 times.

b) Accounts receivable turnover ratio: 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. This ratio is determined by dividing credit sales and average accounts receivable.

$\text{Receivables Turnover Ratio}\text{=}\frac{\text{Net Sales}}{\text{Average}\text{Accounts}\text{Receivables}}$

Calculate the accounts receivable turnover ratio for 2013 and 2012:

Accounts Receivable Turnover Ratio:
Particulars	2013	2012
Net Sales (A)	$9,500	$10,000
Beginning Accounts Receivable (B)	$780	$800
Ending Accounts Receivable (C)	$800	$900
Average Accounts Receivable (D) $\left[\left(\text{B + C}\right)\text{ ÷2}\right]$	$790	$850
Accounts Receivable Turnover Ratio $\left(\text{A ÷ D}\right)$	12 Times	11.76 Times

Table (1)

Therefore, accounts receivable turnover ratio for 2013 and 2012 are 12 times and 11.76 times respectively.

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

$\text{Inventory Turnover Ratio =}\frac{\text{Cost of Goods Sold }}{\text{Average Inventory}}$

Calculate the inventory turnover ratio for 2013 and 2012:

Inventory Turnover Ratio:
Particulars	2013	2012
Cost of Goods Sold (A)	$5,200	$5,500
Beginning Inventory (B)	$620	$650
Ending Inventory (C)	$650	$700
Average Inventory (D) $\left[\left(\text{B +}\text{C}\right)\text{ ÷2}\right]$	$635	$675
Inventory Turnover Ratio $\left(\text{A}\text{÷}\text{D}\right)$	8.18 Times	8.14 Times

Table (2)

Therefore, inventory turnover ratio for 2013 and 2012 are 8.18 times and 8.14 times respectively.

3.

To determine

Calculate the solvency ratios: a) debt-to-equity ratio and b) times interest earned ratio.

Explanation of Solution

a) Debt-equity ratio: The debt-to-equity ratio indicates that the company’s debt as a proportion of its stockholders’ equity.

$\text{Debt-equity ratio}\text{=}\frac{\text{Total}\text{Liabilities}}{\text{Total}\text{Stockholder's}\text{Equity}}$

Calculate the debt-to-equity ratio for 2013 and 2012:

Debt-to-Equity
Particulars	2013	2012
Total Liabilities (A)	$8,300	$8,000
Total Stockholders’ Equity (B)	$2,200	$2,500
Debt-to-Equity (A ÷ B)	3.77	3.2

Table (3)

Therefore, debt-to-equity ratio for 2013 and 2012 are 3.77 and 3.2 respectively.

b) Times Interest Earned Ratio: It is one of the solvency ratios. It is a measure to evaluate the net income for interest payment on debt of a company. It is calculated as follows:

$\text{Times Interest earned ratio}\text{=}\frac{\text{Net Income}\text{+ Interest Expense}\text{+}\text{Income Tax Expense}}{\text{Interest Expense}}$

Calculate the time interest earned ratio for 2013 and 2012:

Times-Interest-Earned
Particulars	2013	2012
Income from Operations (A)	$1,600	$1,700
Interest Expense (B)	$250	$300
Times-Interest-Earned (A ÷ B)	6.4	5.67

Table (4)

Therefore, time-interest earned ratio for 2013 and 2012 are 6.4 and 5.67 respectively.