# Calculating the Intrinsic Value of Preferred Stocks

Valuing preferred stock is one of the easiest things you can learn, which is why I like to teach it to new investors early in their financial education. The simple easy-to-understand formula is one that you'll have no trouble remembering, let alone calculating. The best way to introduce it to you is to dive right in with a fictional scenario so you can see how the math works. Grab a calculator and let's get started.

Imagine that you buy 1,000 shares of preferred stock at $100 per share for a total investment of $100,000. Each share of preferred stock pays a $5 dividend, resulting in a 5% dividend yield ($5 annual dividend divided by $100 preferred stock price = 5% dividend yield). That means that you collect $5,000 in dividend income on your $100,000 investment each and every year. For now, let's pretend that this is a very simple form of preferred stock and not one of the special types, like convertible preferred stock.

Whether you realize it or not, you own what is known as a perpetuity, which is a stream of equal payments paid at regular intervals without an end date. There is a simple formula for valuing perpetuities and basic growth stocks called the Gordon model or the Gordon dividend discount model. The formula is k÷(i-g). The "k" variable is equal to the dividend you receive on your investment, "i" is the rate of return you require on your investment (called the "discount rate"), and "g" is the growth rate of the dividend.

Here are some intrinsic value calculations for the preferred stock:

- If the preferred stock dividend has a 0% growth rate and you had a required rate of return of 10%, you would calculate $5.00÷(0.10-0). That is simplified to $5.00÷0.10 = $50.00. That is, if you wanted to earn a 10% rate of return, you couldn't pay more than $50.00 for the preferred stock. Any price lower than $50.00 will result in a higher return.
- If the preferred stock dividend had a growth rate of 3% per year and you had a required rate of return of 7%, you would calculate $5.00÷(0.07-0.03). The next step is $5.00÷0.04 = $125.00. That is, If you wanted to earn 7% on your preferred stock investment and the dividend increased by 3% forever, you could pay $125.00 per share to hit your return. If you pay more than that, your return will be lower than 7%. If you pay less, your return will be higher than 7%.

### An Interesting Limitation to the Intrinsic Value Calculation for Preferred Stock

One limitation of the intrinsic value formula is that you cannot have a growth rate that exceeds the discount rate or your calculator will return an error or indicate infinity. The reason is that a perpetuity is expected to last forever; from now until Doomsday. If the rate of growth exceeds the required rate of return, the value of the investment is theoretically infinite because no matter what price you pay for your stock, you are someday going to hit your rate of return and exceed it. It may take 75 years or 300 million years but the math isn't concerned with human lifespans!

Other than that interesting quirk, when you are dealing with pure vanilla, simple preferred stock, that really is all there is to it. You now know how to calculate the intrinsic value of preferred stock. Congratulations! Use your new power wisely and start working on a list of stocks that you may want to consider adding to your portfolio.