# Required Rate of Return Models

### The CAPM

\begin{align*}\text{Required return on equity}&= \text{Risk-free rate} \\&+ (\text{Beta} \times \text{Market risk premium})\end{align*}

The CAPM is generally inappropriate for private entities.

### Expanded CAPM

\begin{align*}\text{Required return on equity} &= \text{Risk-free rate} + (\text{Beta} \times \text{Market risk premium}) \\&+ \text{Small stock premium} \\&+ \text{Company-specific risk premium}\end{align*}

### Build-Up Approach

\begin{align*}\text{Required return on equity}& = \text{Risk-free rate} + \text{Equity risk premium} \\&+ \text{Small stock premium} \\&+ \text{Company-specific risk premium} \\&+ \text{Industry risk premium}\end{align*}

The build-up approach is often used when guideline public companies are unavailable.

#### Example: Comparing Required Return Models

Consider the following information:

$$\small{\begin{array}{l|r}\text{Risk-free rate} & 1.25\% \\ \hline \text{Equity risk premium} & 7.50\% \\ \hline\text{Beta} & 1.875 \\ \hline \text{Small stock premium} & 5.00\% \\ \hline\text{Company-specific risk premium} & 1.88\% \\ \hline\text{Industry risk premium} & 1.50\% \end{array}}$$

#### CAPM

\begin{align*} (\text{R}_{\text{E}})&=1.25\%+1.875×7.50\%\\&= 15.31\%\end{align*}

#### Expanded CAPM

\begin{align*}\text{R}_{\text{E}}&=1.25\%+(1.875×7.50\%)+5\%+1.88\%\\&= 22.19\%\end{align*}

#### Build up Approach

\begin{align*}\text{R}_{\text{E}}&=1.25\%+7.50\%+5\%+1.88\%+1.50\%\\&= 17.13\%\end{align*}

LOS 27 (e) Compare models used to estimate the required rate of return to private company equity (for example, the CAPM, the expanded CAPM, and the build-up approach).

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