The Cost of Preferred Stock The cost of preferred stock is the cost associated with raising one more

The Cost of Preferred Stock The cost of preferred stock is the cost associated with raising one more

dollar of capital by issuing shares of preferred stock. As explained in Chapter 17, preferred stock may or may not have a maturity. Preferred stock without a maturity date is called perpetual preferred stock. Con- sider perpetual preferred stock with a fixed dividend rate, where the div- idend is expressed as a percentage of the par value of a share. 2

The value of this type of preferred stock is the present value of all future dividends to be received by the investor. If a share of preferred stock has a 5% dividend (based on a $100 par value) paid at the end of each year, the value of the stock today is the present value of the stream of $5’s forever:

Present value of preferred stock + ------------------- + … + --------------------

------------------ ∑ $5

This series of constant amounts divided by a denominator that is growing at a constant rate collapses to:

Present value of preferred stock = ------

r If the discount rate is 10% per year:

Present value of preferred stock = ----------- = $50

0.10 That is, investors are willing to pay $50 today for the promised stream

of $5 per year since they consider 10% per year to be sufficient compen- 2 The determination of the cost of preferred equity becomes much more complex for

dividend rates that are not fixed or nearly constant. If the dividend rate is adjusted frequently, the preferred shares will trade around their par value and the required rate of return (and hence the cost of capital) will fluctuate as market rates on pre- ferred shares fluctuate.

The Cost of Capital

sation for the time value of money and the risk associated with the per- petual stream of $5 annual dividends.

Let’s rephrase this relationship, letting P p indicate today’s price, which is the present value of the preferred stock, D p indicate the perpetual divi- dend per share per period, and r p indicate the discount rate, which is the cost of preferred stock capital. Then:

p = -------

We can turn this equation around to solve for r p , given P p and D p :

D r = ------- p p

(11-3)

Consider a share of perpetual preferred stock with a price of $100 and a dividend rate of 12% per year:

D p = $100 × 12% = $12 per share P p = $100

We want to solve for the discount rate that equates the discounted value of future dividends with today’s price. This discount rate is the cost of preferred stock, r p , which is also the required rate of return on perpet- ual preferred stock:

r = -------------

0.12 or 12%

But an issuer must pay flotation costs. In this case, the proceeds of the issue would not be $100 per share, but less. If the flotation costs are 2% of the price of the stock when it is issued (thus, $2 per share), the issuer’s proceeds from the sale of a share of preferred stock would be $98, instead of $100. Therefore, the issuer’s all-in-cost of preferred stock is more than 12% because of the flotation costs. We know:

D p = $100 × 12% = $12 per share P p = $98

THE FUNDAMENTALS OF VALUATION

and wish to solve for the issuer’s cost of preferred stock, r p : $12

r p = ---------- = 0.1225 or 12.25% per year

$98 But the investor’s required rate of return on the preferred stock is 12%

per year, since they are willing to pay $100 to get a future perpetual stream of $12 per year.

We can rewrite the equation for the cost of perpetual preferred stock to include flotation costs. Let f represent the percentage of the share’s price that is paid in flotation costs. Then,

D r p = ---------------------- p

(11-4)

Substituting the figures in our example, $12

r = ---------- = 0.1225 or 12.25% per year $100 1 0.02 ( – )

p = ---------------------------------------

Because dividends paid on preferred stock are not deductible as an expense for the issuer’s tax purposes, the cost of preferred stock is not adjusted for taxes—dividends paid on this stock are paid out of after-tax dollars. Therefore, the difference between the investor’s required rate of return and the issuer’s cost of preferred stock is due only to flotation costs.