 # Cost of Preferred Stock in WACC By Yuriy Smirnov Ph.D.

## Definition

The cost of preferred stock is a preferred stockholder’s required rate of return. If a company issues preferred stock, it is referred to as hybrid financing because it has features of both common stock and debt instrument. From one side, preferred stock does not have a maturity date like common stock, but from the other side, it grants a fixed-size dividend like a fixed coupon rate bond.

It is necessary to understand that dividends are not tax deductible, and a company is faced with full costs. No tax adjustment should be performed when calculating the cost of preferred stock.

## Formula

The idea behind preferred stock valuation is the time value of money. Their intrinsic value is equal to the sum of all discounted cash flows in the form of a dividend

 Pps = Dps + Dps + … + Dps (1 + rps)1 (1 + rps)2 (1 + rps)n

where Dps is the preferred dividend, Pps is a stock’s intrinsic value, and rps is the required rate of return.

The formula above can be transformed as follows:

 Pps = Dps rps

The cost of preferred stock in WACC depends on whether the stock is outstanding or is a new issue. Thus, to calculate the cost of preferred stock outstanding, we can use the formula below.

 rps = Dps Pps

In the case of a new issue of preferred stock, we should take into account floatation costs. So, the formula above must be transformed as

 rps = Dps Pps × (1 – F)

where F represents flotation costs expressed as a percentage of the actual selling price.

## Examples

### Example 1

Company A has 2,500,000 shares of preferred stock outstanding with a \$10 face value and an annual fixed dividend rate of 9.25%. The current market price of the security is \$8.25. To find the cost of preferred stock, we should use the first formula mentioned above.

Annual preferred dividend per share = \$10 × 0.0925 = \$0.925

rps = \$0.925 ÷ 8.25 = 11.21%

### Example 2

Company B is planning to raise financing through preferred stock issuing of \$50 par value and a fixed dividend rate of 8.25%. The current market price of analogous shares is \$48.75, and flotation costs are 4.5%. In such a case, we have to use the second formula above.

Annual preferred dividend per share = \$50 × 0.0825 = \$4.125

 rps = \$4.125 = 8.86% \$48.75 × (1 – 0.045)

## Limitations of use

The technique of preferred stock valuation described above is based on the following assumptions:

1. The stock does not have a maturity date.
2. The stock is not convertible.
3. The company pays dividends on a regular basis.

In some circumstances, a company can decide to issue preferred stock with a fixed maturity date. On that date, the stock will be redeemed by the company at a predetermined price. To valuate the cost of such preferred stock, the technique of a fixed coupon rate bond valuation can be applied.

If preferred stock is convertible (can be converted into common stock), the standard technique of valuation can’t be applied. The same concerns cases of irregular dividend payments.