Chapter 13, Problem 24PSB

a)

To determine

Calculate the current ratio for the year 2015.

Explanation of Solution

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:

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

The calculation of current ratio for the year 2015 is as follows:

$\begin{array}{c}\text{Current ratio}=\frac{\text{Current assets}}{\text{Current liabilities}}\\ =\frac{\$107,000,000}{\$28,000,000}\\ =3.82:1\end{array}$

Hence, the current ratio for the year 2015 is 3.82:1.

b)

To determine

Calculate the quick ratio for the year 2015.

Explanation of Solution

Quick ratio:

It is a ratio used to determine a company’s ability to pay back its current liabilities. Liquid assets that are current assets except inventory and prepaid expenses.

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

The calculation of quick ratio for the year 2015 is as follows:

$\begin{array}{c}\text{Quick ratio}=\frac{\text{Quick assets }(1)}{\text{Current liabilities}}\\ =\frac{\$55,000,000}{\$28,000,000}\\ =1.96:1\end{array}$

Hence, the quick ratio for the year 2015 is 1.96:1.

Working note:

The calculation of quick assets for the year 2015 is as follows:

$\begin{array}{c}\text{Quick assets}=\text{Current}\text{Assets}-\text{Inventory}-\text{Prepaid expenses}\\ =\$107,000,000-\$50,000,000-\$2,000,000\\ =\$55,000,000\end{array}$

Hence, the quick assets is $55,000,000.

…… (1)

c)

To determine

Calculate the average days to collect accounts receivable for the year 2015.

Explanation of Solution

Average days to collect accounts receivable:

This ratio is used to determine the number of days a particular company takes to collect accounts receivables. It is calculated by using the formula:

  $\begin{array}{l}\text{Average days to collect}\\ \text{ accounts receivable}\end{array}\}=\frac{\text{365}}{\text{Receivables turnover}}$

The calculation of average days to collect accounts receivable for the year 2015 is as follows:

$\begin{array}{c}\begin{array}{l}\text{Average days to collect}\\ \text{ accounts receivable}\end{array}\}=\frac{\text{365}}{\text{Receivables turnover }}\\ =\frac{365}{3.96\left(2\right)}\\ =92.17\text{ days}\end{array}$

Hence, the average days to collect accounts receivable for the year 2015 is 92.17 days.

Working note:

The calculation of the amount of average accounts receivable for the year 2015:

$\begin{array}{c}\text{Average accounts receivable}=\frac{\left(\begin{array}{l}\text{Ending net }\\ \text{receivables}\end{array}\right)+\left(\begin{array}{l}\text{Beginning net }\\ \text{receivables}\end{array}\right)}{2}\\ =\frac{\$47,000,000+\$44,000,000}{2}\\ =\frac{\$51,000,000}{2}\\ =\$45,500,000\end{array}$

Hence, the amount of average accounts receivable for the year 2015 is $45,500,000.

The calculation of receivables turnover for the year 2015 is as follows:

$\begin{array}{c}\text{Receivables turnover}=\frac{\text{}\text{Net credit sales}}{\text{Average accounts receivables}}\\ =\frac{\$180,000,000}{\$45,500,000}\\ =3.96\text{ times}\end{array}$

Hence, the receivables turn over for the year 2015 is 3.96 times.

…… (2)

d)

To determine

Calculate the inventory turnover for the year 2015.

Explanation of Solution

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:

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

The calculation of inventory turnover ratio for the year 2015 is as follows:

$\begin{array}{c}\text{Inventory turnover}=\frac{\text{Cost of goods sold}}{\text{Average inventory}}\\ =\frac{\$147,000,000}{\$55,000,000\left(3\right)}\\ =2.67\text{ times}\end{array}$

Hence, the inventory turnover ratio for the year 2015 is 2.67 times.

Working note:

The calculation of average inventory for the year 2015 is as follows:

$\begin{array}{c}\text{Average inventory =}\frac{\left(\text{Ending inventory}\right)+\left(\text{Beginning inventory}\right)}{2}\\ =\frac{\$50,000,000+\$60,000,000}{2}\\ =\frac{\$110,000,000}{2}\\ =\$55,000,000\end{array}$

Hence, the average inventory is $55,000,000.

…… (3)

e)

To determine

Calculate the book value per share for the year 2015.

Explanation of Solution

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:

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

The calculation of book value per share for the year 2015 is as follows:

$\begin{array}{c}\begin{array}{l}\text{Book value per share }\\ \text{of common stock}\end{array}\}=\frac{\left[\begin{array}{l}\text{Stockholders' }\\ \text{equity}\end{array}\right]-\left[\begin{array}{l}\text{Preferred }\\ \text{stock}\end{array}\right]}{\text{Outstanding common shares}}\\ =\frac{\$102,000,000-\$20,000,000}{5,000,000\text{ shares}}\\ =\$16.40\text{ per share}\end{array}$

Hence, the book value per share for the year 2015 is $16.40 per share.

f)

To determine

Calculate the earnings per share for the year 2015.

Explanation of Solution

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.

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

The calculation of earnings per share for the year 2015 is as follows:

$\begin{array}{c}\text{Earnings per share}=\frac{\text{Net income}-\text{Preferred dividend}}{\text{Average common shares outstanding}}\\ =\frac{\$6,000,000-\$1,000,000}{5,000,000\text{ shares}}\\ =\$1.00\text{ per share}\end{array}$

Hence, the earnings per share for the year 2015 is $1 per share.

g)

To determine

Calculate the price-earnings ratio for the year 2015.

Explanation of Solution

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.

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

The calculation of price-earnings ratio for the year 2015 is as follows:

$\begin{array}{c}\text{Price/Earnings Ratio}=\frac{\text{Market price per share}}{\text{ Earnings per share}\left(\text{f}\text{.}\right)}\\ =\frac{\$16.00\left(\text{Given}\right)}{\$1.00}\\ =\$16.00\end{array}$

Hence, the price-earnings ratio for the year 2015 is $16.00 per share.

h)

To determine

Calculate the debt to asset ratio for the year 2015.

Explanation of Solution

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:

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

The calculation of debt to assets ratio for the year 2015 is as follows:

$\begin{array}{c}\text{Debt-to-assets ratio}=\frac{\text{Total liabilities }}{\text{Total assets}}\\ =\frac{\$113,000,000}{\$215,000,000}\\ =52.56\%\end{array}$

Hence, the debt to assets ratio for the year 2015 is 52.56%.

i)

To determine

Calculate the return on investment for the year 2015.

Explanation of Solution

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:

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

The calculation of return on investment for the year 2015 is as follows:

$\begin{array}{c}\text{Return on investments}=\frac{\text{Net income }}{\text{Average total assets}}\\ =\frac{\$6,000,000}{\$220,500,000\left(4\right)}\\ =2.72\%\end{array}$

Hence, the return on investment for the year 2015 is 2.72%.

Working notes:

The calculation of the amount of average total assets for year 2015.

$\begin{array}{c}\text{Average total assets =}\frac{\left(\begin{array}{l}\text{Ending }\\ \text{total assets}\end{array}\right)+\left(\begin{array}{l}\text{Beginning }\\ \text{total assets}\end{array}\right)}{2}\\ =\frac{\$215,000,000+\$226,000,000}{2}\\ =\frac{\$441,000,000}{2}\\ =\$220,500,000\end{array}$ (4)

j)

To determine

Calculate the return on equity for the year 2015.

Explanation of Solution

Return on equity ratio:

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:

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

The calculation of return on equity for the year 2015 is as follows:

$\begin{array}{c}\text{Return on equity}=\frac{\text{Net income }}{\text{Average stockholders' equity}}\\ =\frac{\$6,000,000}{\$101,000,000\left(5\right)}\\ =5.94\%\end{array}$

Hence, the return on equity for the year 2015 is 5.94%.

Working notes:

The calculation of average total stockholders’ equity for Year 2015 is as follows:

$\begin{array}{c}\begin{array}{l}\text{Average total }\\ \text{stockholders' equity }\end{array}\}\text{=}\frac{\left(\begin{array}{l}\text{Ending total }\\ \text{stockholders' equity}\end{array}\right)+\left(\begin{array}{l}\text{Beginning total }\\ \text{stockholders' equity}\end{array}\right)}{2}\\ =\frac{\$107,000,000+\$104,000,000}{2}\\ =\frac{\$202,000,000}{2}\\ =\$101,000,000\end{array}$

Hence, the average total stockholders’ equity is $101,000,000.

…… (5)