Chapter 4, Problem 7QP

a.

Summary Introduction

To compute: Return on equity (ROE)

Explanation of Solution

The formula to calculate return on equity is as follows:

$\text{Return on equity}=\frac{\text{Net income}}{\left(\frac{\begin{array}{l}\text{shareholders equity at the end of the year}\\ +\text{share holders equity at thestart of the year}\end{array}}{2}\right)}$

The calculation of return on equity is as follows:

$\begin{array}{c}\text{Return on equity} =\frac{1223}{\left(\frac{9724+9121}{2}\right)}\\ =0.129796\\ =13\%\end{array}$

Hence, the ROE is 13%

b.

Summary Introduction

To compute: Return on assets (ROA)

Explanation of Solution

The formula to calculate return on asset is as follows:

$\text{Return on asset}=\frac{\text{Net income}+\text{Interest expense}\left(1-\text{Tax rate}\right)}{\left(\frac{\text{Total assets at the start of the year}+\text{Total assets at the end of the year}}{2}\right)}$

The calculation of return on capital is as follows:

$\begin{array}{c} \text{ Return on assets}=\frac{1,223+685\times (1-.35)}{\left(\frac{27,714+27,503}{2}\right)}\\ =0.0604\\ =6.04\%\end{array}$

Hence, the ROA is 6.04%

c.

Summary Introduction

To compute: Return on capital (ROC)

Explanation of Solution

The formula to calculate return on capital is as follows:

$\text{Return on capital}=\frac{\text{Net income}+\text{Interest expense}\times \left(1-\text{Tax rate}\right)}{\left(\frac{\begin{array}{l}\left[\begin{array}{l}\text{Long term debt and leases at the start of the year }+\\ \text{shareholders equity at the end of the year}\end{array}\right]+\\ \left[\begin{array}{l}\text{Long term debt and leases at the end of theyear}+\\ \text{shareholders equity at the end of theyear}\end{array}\right]\end{array}}{2}\right)}$

The calculation of return on equity is as follows:

$\begin{array}{c}\text{Return on capital}=\frac{1,223+685\times (1-.35)}{\frac{[(7,018+9,724)+(6,833+9,121)]}{2}}\\ =0.1020\\ =10.20\%\end{array}$

Hence, the ROC is 10.20%

d.

Summary Introduction

To compute: Days in inventory.

Explanation of Solution

The formula to calculate days in inventory is as follows:

$\text{Days in inventory}=\frac{\text{Inventory in the start of the year}}{\left(\frac{\text{Cost of goods sold}}{365}\right)}$

.

The calculation of days in inventory is as follows:

 $\begin{array}{c}\text{Days in inventory}==\frac{238}{\left(\frac{4,060}{365}\right)}\\ =21.40\text{ days}\end{array}$

Hence, the days in inventory is 21.40 days

e.

Summary Introduction

To compute: Inventory turn over

Explanation of Solution

The formula to calculate inventory turnover is as follows:

$\text{Inventory turnover}=\frac{\text{Cost of goods sold}}{\text{Inventory at start of year}}$

The calculation of inventory turnover is as follows:

$\begin{array}{c}\text{Inventory turnover}==\frac{4,060}{\frac{(187+238)}{2}}\\ =19.11\end{array}$

Hence, the inventory turnover is 19.11

f.

Summary Introduction

To compute: Average collection period(ACP)

Explanation of Solution

The formula to calculate average collection period is as follows:

$\text{Average collection period }=\frac{\text{Receivables at start of year}}{\text{Average daily sales}}$

The calculation of average collection period is as follows:

$\begin{array}{c} \text{Average collection period}=\frac{2,490}{\left(\frac{13,193}{365}\right)}\\ =68.89\text{ days}\end{array}$

Hence, the ACP is 68.89 days.

g.

Summary Introduction

To compute: Operating profit margin (OPM)

Explanation of Solution

The formula to calculate operating profit margin is as follows:

$\text{Operating profit margin}==\frac{\text{Net income }+\text{ After-tax interest}}{\text{Sales}}$

The calculation of operating profit margin is as follows:

$\begin{array}{c}\text{Operating profit margin}=\frac{1,223+685\times (1-.35)}{13,193}\\ =0.1264\\ =12.64\%\end{array}$

Hence, the OPM is 12.64%

h.

Summary Introduction

To compute: Long term debt ratio

Explanation of Solution

The formula to calculate operating profit margin is as follows:

$\text{Long term debt ratio}=\frac{\text{Long term debt and leases at the end of the year}}{\left(\begin{array}{l}\text{long term debt and leases at the end of the year }\\ +\text{shareholders equity at the end of the year}\end{array}\right)}$

The calculation of long term debt ratio is as follows:

$\begin{array}{c} \text{Long-term debt ratio}=\frac{7,018}{7,018+9,724}\\ =0.42\end{array}$

Hence the long term debt ratio is 0.42

i.

Summary Introduction

To compute: Total debt ratio

Explanation of Solution

The formula to calculate total debt ratio is as follows:

$\text{Total debt ratio}=\left(\frac{\begin{array}{l}\text{Total current liabilities at the end of the year}+\\ \text{Long term debt and leases at the end of the year}+\\ \text{Other long term liabilities at the end of the year}\end{array}}{\text{Total assets at the end of the year}}\right)$

The calculation of total debt ratio is as follows:

$\begin{array}{c} \text{Total debt ratio}=\frac{4,794+7,018+6,178}{27,714}\\ =0.65\end{array}$

Hence the total debt ratio is 0.65

j.

Summary Introduction

To compute: Times interest earned

Explanation of Solution

The formula to calculate times interest earned is as follows:

$\text{Times interest earned}=\frac{\text{EBIT}}{\text{Interest expense}}$

The calculation of times interest earned is as follows:

$\begin{array}{c}\text{Times interest earned}=\frac{2,566}{685}\\ =3.75\end{array}$

Hence the time interest earned is 3.75

k.

Summary Introduction

To compute: Cash coverage ratio

Explanation of Solution

The formula to calculate cash coverage ratio is as follows:

$\text{Cash coverage ratio}=\frac{\left(\text{EBIT+Depreciation}\right)}{\text{Interest expense}}$

The calculation of cash coverage ratio is as follows:

$\begin{array}{c} \text{ Cash coverage ratio}==\frac{2,566+2,518}{685}\\ =7.42\end{array}$

Hence the cash coverage ratio is 7.42

l.

Summary Introduction

To compute: Current ratio

Explanation of Solution

The formula to calculate current ratio is as follows:

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

The calculation of current ratio is as follows:

$\begin{array}{c} \text{ Current ratio}=\frac{3,525}{4,794}\\ =0.74\end{array}$

Hence the current ratio is 0.74

m.

Summary Introduction

To compute: Quick ratio

Explanation of Solution

The formula to calculate quick ratio is as follows:

$\text{Quick ratio}=\frac{\text{Cash + Marketable securities + Receivables}}{\text{Current liabilities}}$

The calculation of quick ratio is as follows:

$\begin{array}{c} \text{Quick ratio}=\frac{89+2,382}{4,794}\\ =0.52\end{array}$

Hence the quick ratio is 0.52