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.

Example: Calculating the Value of a Noncallable Perpetual Preferred Stock

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 a $100 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

The correct answer is C.

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

Reading 23: Discounted Dividend Valuation

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