Chapter 28, Problem 9PS

Financial ratios* As you can see, someone has spilled ink over some of the entries in the balance sheet and income statement of Transylvania Railroad (Table 28.9). Can you use the following information to work out the missing entries? (Note: For this problem, use the following definitions: inventory turnover = COGS/average inventory; receivables collection period = average receivables/|sales/365|.)

• Long-term debt ratio: .4.
• Times-interest-earned: 8.0.

• Current ratio: 1.4.
• Quick ratio: 1.0.
• Cash ratio: .2.
• Inventory turnover: 5.0.
• Receivables collection period: 73 days. Tax rate = .4.

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 is $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 is $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 is $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 is $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 is $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 is $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,