# Preferred Stock Valuation

The value of a preferred stock equals the present value of its future dividend payments discounted at the required rate of return of the stock. In most cases the preferred stock is perpetual in nature, hence the price of a share of preferred stock equals the periodic dividend divided by the required rate of return.

Preferred stock has characteristics of both equity and debt. Debt-like feature of a typical preferred stock issue is the fixed preferred dividend rate that preferred stock pays over its life while its equity-like feature is its perpetual existence. They are riskier than bonds and other form of debt and safer than the common stock. This is because holders of preferred stock have preference over common stockholders in distribution of dividends and winding-up proceeds, but they rank below debt-holders because interest expense is paid before any dividends can be paid to preferred stockholders.

## Formula

The following formula can be used to determine value of a share of standard preferred stock:

$$V_P=\frac{D_P}{r}=\frac{P\times d_p}{r}$$

Where VP is the value/price of a share of preferred stock, DP is the annual dividend per share of preferred stock, r is the required rate of return, P is the par value per share of preferred stock and dp is the annual preferred dividend rate.

DP equals the par value (also called face value) of the stock multiplied by the stated dividend rate. The required rate of return reflects the market assessment of the risk inherent in the preferred stock.

Due to the perpetual nature of preferred stock, the fixed periodic dividends form a perpetuity. Where the preferred stock dividends grow at a constant rate g, its value equals the present value of a growing perpetuity.

Where a preferred stock is callable or convertible, its pricing is different because of the embedded options.

## Example

Determine the value of a share of a $1,000 par value preferred stock that pays 8% dividends at the end of each year assuming the required rate of return on the preferred stock is (a) 8.5% and (b) 7.5%. The value of a preferred stock at 8.5% required return equals$941.18.

$$V_P=\frac{1,000\times8\%}{8.5\%}=941.18$$

However, the value of preferred stock at 7.5% required return is

$$V_P=\frac{1,000\times8\%}{7.5\%}=1,066.67$$

There is a basic relationship between the required rate of return and the stated preferred dividend rate. If the required rate of return is higher than the preferred dividend rate, the preferred stock will have a value below its par and vice versa. The value of a preferred stock will match the par value only when the preferred dividend rate and the required rate of return are equal.