Chapter 28, Problem 20PS

Summary Introduction

To determine: Various financial ratios to complete the balance sheet.

Explanation of Solution

Given information:

Long term debt ratio is 0.4

Times-interest earned is 8.0

Current ratio is 1.4

Cash ratio is 0.2

Inventory turnover ratio is 5.0

Tax rate is 0.40

Quick ratio is 1.0

Calculation of financial ratios:

$\begin{array}{c}\text{Total assets}=\text{Total liabilities}+\text{equity}\\ =\$115\end{array}$

Therefore, total assets are $115

$\begin{array}{c}\text{Total}\text{current}\text{liabilities}=\text{Notes}\text{payable}+\text{accounts}\text{payables}\\ =\$25+\$30\\ =\$55\end{array}$

Therefore, total current liabilities are $55

$\begin{array}{c}\text{Total}\text{current}\text{assets}=\text{Current}\text{ratio}\times \text{total}\text{current}\text{liabilities}\\ =1.4\times \$55\\ =\$77\end{array}$

Therefore, total current assets are $77

$\begin{array}{c}\text{Cash}=\text{Cash ratio}\times \text{total}\text{current}\text{liabilities}\\ =0.2\times \$55\\ =\$11\end{array}$

Hence, cash is $11

$\begin{array}{c}\text{Accounts}\text{receivables}=\left(\text{Quick}\text{ratio×total}\text{current}\text{liabilities}\right)-\text{cash}\\ =\left(1\times \$55\right)-\$11\\ =\$44\end{array}$

Therefore, accounts receivables are $44

$\begin{array}{c}\text{Inventory}=\text{Total}\text{current assets}-\text{cash}-\text{accounts}\text{receivables}\\ =\$77-\$11-\$44\\ =\$22\end{array}$

Therefore, inventory is $22

$\begin{array}{c}\text{Fixed assets}=\text{Total assets}-\text{total current assets}\\ =\$115-\$77\\ =\$38\end{array}$

Therefore, fixed assets are $38

$\begin{array}{c}\text{Long-term debt}+\text{equity}=\text{Total}\text{assets}-\text{total}\text{current}\text{liabilities}\\ =\$115-\$55\\ =\$60\end{array}$

Therefore, long-term debt and equity is $60

$\begin{array}{c}\text{Long-term debt}=\left(\text{long-term}\text{debt}+\text{equity}\right)-\text{long-term}\text{debt ratio}\\ =\$60\times 0.40\\ =\$24\end{array}$

Therefore, long-term debt is $24

$\begin{array}{c}\text{Equity}=\left(\text{long-term}\text{debt}+\text{equity}\right)-\text{long-term}\text{debt }\\ =\$60-\$24\\ =\$36\end{array}$

Therefore, equity is $36

For completing the balance sheet the following ratios are needed,

$\begin{array}{c}\text{Average}\text{inventory}=\frac{\left(\text{Begining}\text{inventory}+\text{ending}\text{inventory}\right)}{2}\\ =\frac{\left(\$22+\$26\right)}{2}\\ =\$24\end{array}$

Therefore, average inventory is $24

$\begin{array}{c}\text{Inventory}\text{turnover}=\frac{\text{Cost}\text{of}\text{goods}\text{sold}}{\text{Average}\text{inventory}}\\ \text{COGS}=5.0\times \$24\\ =\$120\end{array}$

Therefore, cost of goods sold is $120

$\begin{array}{c}\text{Average}\text{receivables}=\frac{\left(\text{Begining}\text{receivables}+\text{ending}\text{receivables}\right)}{2}\\ =\frac{\left(\$34+\$44\right)}{2}\\ =\$39\end{array}$

Therefore, average receivables are $39

$\begin{array}{c}\text{Receivables collection period}=\frac{\text{Average}\text{receivables}}{\left[\frac{\text{Sales}}{365}\right]}\\ \text{Sales}=\left[\frac{\$39}{\$73}\right]\times 365\\ =\$195\end{array}$

Therefore, sales are $195

$\begin{array}{c}\text{EBIT}=\text{Sales}-\text{COGS}-\text{selling}\text{expenses}-\text{depreciation}\\ =\$195-\$120-\$10-\$20\\ =\$45\end{array}$

Therefore, EBIT is $45.

$\begin{array}{c}\text{Interest}=\frac{\text{EBIT}}{\text{Times}\text{interest}\text{earned}}\\ =\frac{\$45}{\$8}\\ =\$5.625\end{array}$

Therefore, interest is $5.625

$\begin{array}{c}\text{Earnings before tax}=\text{EBIT}-\text{interest}\\ =\$45-\$5.625\\ =\$39.375\end{array}$

Therefore, interest is $39.375

$\begin{array}{c}\text{Tax}=\text{Earnings}\text{before}\text{tax}\times \text{tax}\text{rate}\\ =\$39.375\times 0.40\\ =\$15.75\end{array}$

Therefore, tax is $15.75

$\begin{array}{c}\text{Earnings available}\text{for}\text{common}\text{stock}=\text{Earnings before tax}-\text{tax}\\ =\$39.375-\$15.75\\ =\$23.63\end{array}$

Therefore, company balance sheet is as follows,