# Calculating the Intrinsic Value of Preferred Stocks

Valuing a simple preferred stock is one of the easiest things to learn, which is why new investors often learn about it early in their financial education. The easy-to-understand formula is one that you'll have no trouble calculating, remembering, and applying to your investment considerations. The best way to introduce it to you is to walk through a fictional scenario so you can see how the math works.

## Preferred Stock vs. Common Stock

If you're new to investing, you might not be aware that not all stocks are the same type of security. The two primary kinds of stocks are common stock and preferred stock. The differences between the two have to do with voting rights and dividend payments.﻿﻿﻿﻿ However, the specific rights for the preferred and common stock will vary by the company issuing the stock.

When it comes time to vote for new board members of a company, for example, investors with common stock will likely be the ones weighing in. Each share of common stock usually comes with a voting right. The more shares you own, the more you can influence company-wide votes. Preferred stock usually comes without voting rights, so no matter how many shares you own, you won't have a say in how the business operates.

While preferred stock doesn't entitle an investor to voting rights, those investors do have preference over common stock investors when it comes to dividends and liquidation. The preferred stock will receive dividend payments before common stock. If the company declares bankruptcy, investors with preferred stock will receive liquidated assets before investors with common stock. However, if the company issues bonds, bondholders will receive assets before investors with preferred stock.

## Preferred Stock Valuation Example

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 (you get this percentage by dividing the \$5 dividend by the \$100 stock price). That means that you collect \$5,000 in dividend income on your \$100,000 investment every year. For this example, assume that this is a simple form of preferred stock and not one of the special types, like convertible preferred stock.

## The Formula

Since the example involves a simple form of preferred stock, you own what is known as a "perpetuity"—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 Growth model or the Gordon dividend discount model.

The formula is "k ÷ (i - g) = v."﻿﻿﻿﻿ In this equation:

• "k" is equal to the dividend you receive on your investment
• "i" is the rate of return you require on your investment (also called the discount rate)—you can adjust this figure to fit your investment goals
• "g" is the average annual growth rate of the dividend
• "v" is the value of the stock that will deliver your desired return

## The Calculation

Here are some intrinsic value calculations for simple preferred stock.

If the preferred stock has an annual dividend of \$5 with a 0% growth rate (the company never increases or decreases the dividend), and you require a rate of return of 10%, you would calculate:

• \$5 ÷ (0.10 - 0)
• Simplified, this becomes \$5 ÷ 0.10 = \$50
• In this scenario, if you wanted to earn a 10% rate of return, you couldn't pay more than \$50 for the preferred stock. On the other hand, buying the stock at a price lower than \$50 will result in a higher return.

Now let's say that preferred stock had an average dividend growth rate of 3% per year, and you require a rate of return of 7%. You would calculate:

• \$5 ÷ (0.07 - 0.03)
• Simplified, this becomes \$5 ÷ 0.04 = \$125
• In this scenario, if you wanted to earn 7% on your preferred stock investment, and you expect the dividend to increase by 3% annually, you could pay \$125 per share and still hit your return goals. If you pay more than that, your return will be lower than 7%. If you pay less, your return will be higher than 7%.

## A Limitation to the Intrinsic Value Calculation

One limitation of the intrinsic value formula is that you cannot have a growth rate that exceeds your desired rate of return. If you do, your calculator will return an error or indicate infinity. That's because a perpetuity is expected to last forever—from now until the end of time.

If the rate of growth exceeds the required rate of return, the value of the investment is theoretically infinite. No matter what price you pay for the preferred stock, you are someday going to hit your rate of return and exceed it. What the equation doesn't account for is the human lifespan, and whether the timeline for achieving the required rate of return is feasible.

Other than that one interesting quirk, this equation is all you need to calculate the intrinsic value of a simple preferred stock.

### Article Sources

1. Office of Investor Education and Advocacy. "Stocks." Accessed Jan. 27, 2020.

2. NYU Stern School of Business. "The Stable Growth DDM: Gordon Growth Model," Page 1. Accessed Jan. 27, 2020.