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Assume the following data for Cable Corporation and Multi-Media Incorporated.

\begin{tabular}{lrc}
& \begin{tabular}{c}
Cable \\
Corporation
\end{tabular} & \begin{tabular}{c}
Multi-Media \\
Incorporated
\end{tabular} \\
\hline Net income & [tex]$\$[/tex] 38,200[tex]$ & $[/tex]\[tex]$ 172,000$[/tex] \\
Sales & [tex]$323,000$[/tex] & [tex]$2,020,000$[/tex] \\
Total assets & [tex]$475,000$[/tex] & [tex]$958,000$[/tex] \\
Total debt & [tex]$156,000$[/tex] & [tex]$475,000$[/tex] \\
Stockholders' equity & [tex]$319,000$[/tex] & [tex]$483,000$[/tex]
\end{tabular}

a. Compute return on stockholders' equity for both firms. Note: Input your answers as a percent rounded to 2 decimal places.

\begin{tabular}{|l|l|l|}
\hline & \multicolumn{2}{|c|}{\begin{tabular}{c}
Return on \\
Stockholders' \\
Equity
\end{tabular}} \\
\hline Cable Corporation & & [tex]$\%$[/tex] \\
\hline Multi-Media Incorporated & & [tex]$\%$[/tex] \\
\hline
\end{tabular}

Sagot :

GinnyAnswer
To compute the return on stockholders' equity (ROE) for both Cable Corporation and Multi-Media Incorporated, we use the formula:

[tex]\[ \text{ROE} = \left( \frac{\text{Net Income}}{\text{Stockholders' Equity}} \right) \times 100 \][/tex]

### Step-by-Step Solution:

1. Identify the given data:
- For Cable Corporation:
- Net income = [tex]$38,200 - Stockholders' equity = $[/tex]319,000

- For Multi-Media Incorporated:
- Net income = [tex]$172,000 - Stockholders' equity = $[/tex]483,000

2. Compute the ROE for Cable Corporation:
[tex]\[ \text{ROE}_{\text{Cable}} = \left( \frac{38,200}{319,000} \right) \times 100 \][/tex]
The computation gives us approximately:
[tex]\[ \text{ROE}_{\text{Cable}} = 11.97\% \][/tex]

3. Compute the ROE for Multi-Media Incorporated:
[tex]\[ \text{ROE}_{\text{Multi-Media}} = \left( \frac{172,000}{483,000} \right) \times 100 \][/tex]
The computation gives us approximately:
[tex]\[ \text{ROE}_{\text{Multi-Media}} = 35.61\% \][/tex]

### Results:

- Cable Corporation:
[tex]\[ \text{ROE} = 11.97\% \][/tex]

- Multi-Media Incorporated:
[tex]\[ \text{ROE} = 35.61\% \][/tex]

The return on stockholders' equity for Cable Corporation is [tex]\( 11.97\% \)[/tex] and for Multi-Media Incorporated is [tex]\( 35.61\% \)[/tex].
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