# Equation for the Present Value of Preferred Stock

By: Eric Bank, MBA, MS Finance The type of preferred stock determines which equation to use. Comstock Images/Comstock/Getty Images

A corporation issues preferred stock to raise cash for operations and growth. You might wish to invest in preferred stock if you are looking for dividend income. The present value of an investment is the value of future cash flows discounted by an interest rate. The result is what you would be willing to pay for the investment. The present value calculation you use on preferred stock depends on whether the stock is redeemable.

## Preferred Stock

Preferred stock is equity, not debt. However, it resembles debt in that it pays a fixed amount of cash periodically. The dividend yield is the annual dividend amount divided by the stock price. Most preferred stock is perpetual -- it goes on paying dividends forever. Some preferred stocks are callable, in which case the issuer may recall the shares for a set price after a certain date. Some preferred stocks have a maturity date on which the company redeems the shares. If a company goes bankrupt, holders of preferred stock receive liquidation proceeds ahead of common stockholders but after bondholders.

## Perpetual Preferred

The present value of perpetual preferred stock treats the shares as a perpetuity: An infinite number of dividend payments stretch out into the future. The formula is the fixed dividend amount divided by the discount factor. For example, suppose you purchase 100 shares of a perpetual preferred stock that pays an annual \$4 dividend. You bought the stock for \$50 a share, so the dividend yield is 8 percent. The present value is \$4 divided by 0.08, or \$50, which is precisely the amount you paid.

## Redeemable Preferred

Redeemable preferred is stock that is callable or has a maturity date, so you price it the same way you price a bond, using an equation that sums the present value of two terms. You need to determine the number of dividend payments until redemption, the amount of each payment and the dividend yield per period. Assume you are considering stock that will mature in 10 years for \$1,000. Each semiannual dividend payment is \$50, and you require a semiannual dividend yield of 6 percent. You plug these numbers into the present value formula.

## Equation

The present value of the example stock uses two terms. Let X equal 1 plus the required semiannual yield raised to the number of payments until redemption, or 1.06 raised to the power of 20, which in the example is 3.207. The first term of the present value is (1 minus (1 divided by X)) divided by the semiannual dividend yield and then multiplied by the dividend payment. This is equal to (1 minus (1 divided 3.207)) divided by 0.06, all multiplied by \$50, or \$573.50. The second term is the redemption amount divided by X, or \$1,000 divided by 3.207, which equals \$311.82. The total present value of the stock is \$573.50 plus \$311.82, or \$885.32.