 # Value of a Noncallable Perpetual Preferred Stock

Firms with no additional opportunities to generate returns above the required rate of return should distribute all of their earnings in dividends. Their securities have a specified fixed dividend rate and have no maturity date. As dividends on these securities are fixed, and $$g$$ equals 0, their value can be computed as:

$$\text{V}_{0}=\frac{\text{D}_{\text{p}}}{\text{r}_{\text{p}}}$$

Where:

$$\text{D}_{\text{p}}=$$ Perpetual dividend.

$$\text{r}_{\text{p}}=$$ Cost of preferred equity.

ABC Ltd. has a noncallable perpetual preferred stock outstanding with a dividend of 10% (based on an issue at par of 100). Given that the investors’ required rate of return for holding these shares is 12%, the current value of the shares is closest to: #### Solution \begin{align*}\text{Value of perpetual preferred shares}&=\frac{\text{D}_{\text{p}}}{\text{r}_{\text{p}}}\\ \\ \text{Where } \text{D}_{\text{p}}&=10\% \times100=\10 \\ \\ \text{Value of perpetual preferred shares}&=\frac{\10}{0.12}=83.33 \end{align*} ## Question A company has a100 par 6% fixed-rate perpetual preferred stock. Given a required rate of return of 8%, the current value of the security is closest to:

1. $55. 2.$70.
3. \$75.

#### Solution

\begin{align*}\text{V}_{0}&=\frac{\text{D}_{\text{p}}}{\text{r}_{\text{p}}}\\ \\&=\frac{6.00}{0.08}=75\end{align*}

LOS 23 (d) Calculate the value of noncallable fixed-rate perpetual preferred stock.

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