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Question 18.ss.2: You have the following information for a company you are val...

You have the following information for a company you are valuing and for a comparable company:

\begin{matrix}\bold{Comparable \ company} && \bold{Company \ you \ are \ valuing} \\ \text{Stock price}=\$23.45 && \text{Value of debt}=\$3.68 \ \text{million} \\ \text{Number of shares outstanding}=6.23 \ \text{million} && \text{Est.EBITDA next year}=\$4.4 \ \text{million} \\ \text{Value of debt}=\$18.45 \ \text{million} && \text{Est.income next year}=\$1.5 \ \text{million} \\ \text{Est.EBITDA next year}=\$17.0 \ \text{million} \\ \text{Est.income next year}=\$5.3 \ \text{million} \end{matrix}

Estimate the enterprise value of the company you are evaluating using the P/E and enterprise value/EBITDA multiples.

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The P/E and enterprise value/EBITDA multiples for the comparable company are:

\begin{matrix} \left(\frac{P}{E}\right) _{\text{Comparable}} & = & \left(\frac{\text{Stock price}}{\text{Earnings per share}}\right)_{\text{Comparable}} \\ \\ & = & \frac{\$23.45 \text{per share}}{\$5.3 \ \text{million}/6.23 \ \text{million shares}} \\ \\ & = & 27.6 \end {matrix}

 

\begin{matrix} \left(\frac{\text{Enterprise value}}{EBITDA}\right)_{\text{Comparable}} & = & \left(\frac{V_D+V_E}{EBITDA}\right)_{\text{Comparable}} \\ \\ & = & \frac{\$18.45 \ \text{million}+(\$23.45 \text{per share}\times 6.23  \text{million  shares})}{\$17.0 \ \text{million}} \\ \\ & = &9.68 \end{matrix}

Using the P/E multiple, we can calculate the value of the equity as:

\begin{matrix} V_E &=& \left(\frac{P}{E}\right)_{\text{Comparable}}\times \text{Net income}_{\text{Company being valued}} \\ \\ &=&27.6\times \$1.5  \text{million} \\ \\ &=&\$41.4 \text{ million} \end{matrix}

which suggests an enterprise value of:

V_F=V_E+V_D=\$41.4 \text{million}+\$3.68 \text{ million}=\$45.08 \text{ million}

Using the enterprise/EBITDA multiple, we obtain:

\begin{matrix} V_F &=& \left(\frac{\text{Enterprise value}}{EBITDA}\right)_{\text{Comparable}} \times EBITDA_{\text{Company being valued}} \\ \\ &=&9.68\times \$4.4 \text{million} \\ \\ &=&\$42.59 \text{ million} \end{matrix}

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