Chapter 3, Problem 28QP

Ratios and Fixed Assets. The Smathers Company has a long-term debt ratio (i.e., the ratio of long-term debt to long-term debt plus equity) of .45 and a current ratio of 1.30. Current liabilities are $2,435, sales are $11,610, profit margin is 9 percent, and ROE is 12.8 percent. What is the amount of the firm’s net fixed assets?

Summary Introduction

To calculate: The net fixed assets of the firm.

Introduction:

A fixed asset is the long-term tangible piece of property that a firm owns and utilizes for the production. The firm is not expected to consume or convert the fixed asset into cash within a year. The fixed assets are collectively termed as “plant”.

The process of analyzing and calculating the financial ratios in order to evaluate the performance of the firm and to find the actions that are necessary to improve the firm’s performance is known as ratio analysis.

Answer to Problem 28QP

The net fixed asset is $14,111.83.

Explanation of Solution

Given information:

The Company S has a long-term debt ratio of 0.45, current liabilities of $2,435, profit margin of 9%, current ratio of 1.30, sales of $11,610, and return on equity of 12.8%

Note: The net fixed assets of the firm can be found with the help of the current assets and total assets (Total assets = Current assets + Net fixed assets). The current asset can be solved by utilizing the given current liabilities and the current ratio.

Formula to calculate the current asset:

$\begin{array}{c}\text{Current ratio}=\frac{\text{Current assets}}{\text{Current liabilities}}\\ \text{Current asset}=\text{Current ratio}\times \text{Current liabilities}\end{array}$

Note: The current assets can be calculated by using the formula of current ratio.

Compute the current asset:

$\begin{array}{c}\text{Current ratio}=\frac{\text{Current assets}}{\text{Current liabilities}}\\ \text{Current asset}=\text{Current ratio}\times \text{Current liabilities}\\ \text{=1}\text{.30}\times \text{\$2,435}\\ \text{=\$3,165}\text{.50}\end{array}$

Hence, the current asset is $3,165.50.

Note: To find the total assets, it is essential to find the total equity and the total debt from the given information. Thus, the net income is found using the formulae of the profit margin.

Formula to calculate the net income:

$\text{Profit margin}=\frac{\text{Net income}}{\text{Sales}}$

Compute the net income:

$\begin{array}{c}\text{Profit margin}=\frac{\text{Net income}}{\text{Sales}}\\ \text{Net income}=\text{Profit margin}\times \text{Sales}\\ =0.09\times \$11,610\\ =\$1,044.90\end{array}$

Hence, the net income is $1,044.90.

Formula to calculate the Total equity:

$\begin{array}{c}\text{Return on equity}=\frac{\text{Net income}}{\text{Total equity}}\\ \text{Total equity}=\frac{\text{Net income}}{\text{Return on equity}}\end{array}$

Note: The total equity can be calculated by using the calculated net income figure as an input in the return on equity.

Compute the Total equity:

$\begin{array}{c}\text{Return on equity}=\frac{\text{Net income}}{\text{Total equity}}\\ \text{Total equity}=\frac{\text{Net income}}{\text{Return on equity}}\\ =\frac{\$1,044.90}{0.128}\\ =\$8,163.28\end{array}$

Note: The total equity 12.8% is taken as 0.128.

Hence, the total equity is $8,163.28.

Formula to calculate the long-term debt:

$\text{Long-term debt ratio}=\frac{\text{Long-term debt}}{\left(\text{Long-term debt}+\text{Total equity}\right)}$

Note: The long-term debt ratio is given as 0.45. So, with the help of the long-term debt ratio, an equation can be computed.

Compute an equation using the formula of long-term debt ratio:

$\begin{array}{c}\text{Long-term debt ratio}=\frac{\text{Long-term debt}}{\left(\text{Long-term debt}+\text{Total equity}\right)}\\ 0.45=\frac{\text{Long-term debt}}{\left(\text{Long-term debt}+\text{Total equity}\right)}\end{array}$

Note: The following equation can be computed by inverting both the sides.

$\begin{array}{c}\text{Long-term debt ratio}=\frac{\text{Long-term debt}}{\left(\text{Long-term debt}+\text{Total equity}\right)}\\ \frac{1}{0.45}=\frac{\left(\text{Long-term debt}+\text{Total equity}\right)}{\text{Long-term debt}}\\ \frac{1}{0.45}=\frac{\text{Long-term debt}}{\text{Long-term debt}}+\frac{\text{Total equity}}{\text{Long-term debt}}\\ \frac{1}{0.45}=1+\left(\frac{\text{Total equity}}{\text{Long-term debt}}\right)\end{array}$

Now the calculated total equity is substituted in the equation to find the long-term debt.

$\begin{array}{c}\frac{1}{0.45}=1+\left(\frac{\text{Total equity}}{\text{Long-term debt}}\right)\\ 2.222=1+\left(\frac{\$8,163.28}{\text{Long-term debt}}\right)\\ 2.222-1=\left(\frac{\$8,163.28}{\text{Long-term debt}}\right)\\ 1.222=\left(\frac{\$8,163.28}{\text{Long-term debt}}\right)\end{array}$

$\begin{array}{l}\text{Long-term debt}=\frac{\$8,163.28}{1.222}\\ \text{Long-term debt}=\$6,679.05\end{array}$

Hence, the long-term is $6,679.05.

Formula to calculate the total debt:

$\text{Total debt}=\text{Current liabilities}+\text{Long-term debt}$

Compute the total debt:

$\begin{array}{c}\text{Total debt}=\text{Current liabilities}+\text{Long-term debt}\\ =\$2,435+\$6,679.05\\ =\$9,114.05\end{array}$

Hence, the total debt is $9,114.05.

Note: With the help of total debt, the total debt and equity can be found which is equal to the total assets.

Formula to calculate the total assets:

$\text{Total assets}=\text{Total debt}+\text{Total equity}$

Compute the total assets:

$\begin{array}{c}\text{Total assets}=\text{Total debt}+\text{Total equity}\\ =\$9,114.05+\$8,163.28\\ =\$17,277.33\end{array}$

Hence, the total asset is $17,277.33.

Formula to calculate the net fixed assets:

$\text{Net fixed assets}=\text{Total assets}-\text{Current assets}$

Compute the net fixed assets:

$\begin{array}{c}\text{Net fixed assets}=\text{Total assets}-\text{Current assets}\\ =\$17,277.33-\$3,165.50\\ =\$14,111.83\end{array}$

Hence, the net fixed asset is $14,111.83.