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Preferred stock is a special type of company stock which brings additional benefits. The cost of preferred stock depends on the context and who the cost applies to. Most commonly, the phrase refers to the cost to the company in issuing the stock. It could also mean the purchase price for the current and future holders of the stock. The cost of preferred stock can also be an opportunity cost.
Preferred stock is different from common stock in several ways. Holders are first in line for any dividend payments. Holders also get priority in receiving their money back if the company goes into liquidation. This guarantee of receiving some or all the purchase price back means preferred stock is a mix of equity security, like common stock, and a debt security, like a bond.
The cost of preferred stock to the company is effectively the price it pays in return for the income it gets from issuing and selling the stock. Stated most simply, the cost is the amount of dividend paid on the stocks divided by the issue price. In other words, it's the amount of money the company pays out in a year divided by the lump sum they got from issuing the stock. That effectively makes the cost a form of interest rate the company pays in return for getting ahold of the money from the stock issue. This figure could thus be compared to the interest rate the company would pay if they instead issued bonds to raise money or simply borrowed it from a financial institution.
For investors, the cost of preferred stock, once it has been issued, will vary like any other stock price. That means it will be subject to supply and demand in the market. In theory at least, preferred stock may be seen as more valuable than common stock as it has a greater likelihood of paying a dividend and offers a greater deal of security if the company folds.
It is also possible to refer to the cost of preferred stock in more general terms. In this sense it is the opportunity cost: what you give up by having the preferred stock. Calculating this cost is much more difficult, as it is more hypothetical. For example, one cost would be that the holder of preferred stock usually has no voting rights. Whether this is an important cost depends on the individual. Another cost is that the preferred stock may not rise in price as quickly as common stock, so the cost is the loss of potential profit after selling.
It seems to me that something called "preferred stock" or "preferred securities", or anything with the word "preferred" would be only positive, but it sounds from this article like having the preferred stock might do more bad than good in some cases.