Intrinsic Value of a Preferred Stock

The intrinsic value of a non-callable, non-convertible preferred stock can be calculated in much the same way as a share of common stock, except the expected sales price is replaced by the par value of the preferred shares.

$$ V_0=\sum_{t=1}^n\frac{D_t}{(1+r)^t}+\frac{F}{(1+r)^n}$$

Where:

V₀ = present value of a share of stock today

D_t = expected dividend in year t

r = required return on the stock

F = par value of the preferred stock

n = years to maturity

Question

ABC’s 5% dividend-paying preferred shares have a par value of $100. The required rate of return on preferred shares with the same rating is 7% as of the valuation date. The preferred shares will mature in ten years.

All else being equal, if the preferred shares instead matured in 15 years, how would the intrinsic value of ABC’s preferred shares change?

1. The longer maturity would increase current valuation.
2. The longer maturity would decrease current valuation.
3. The longer maturity would not change current valuation.

Solution

The correct answer is B.

The intrinsic value of preferred shares is influenced by the time to maturity and the required rate of return. When the dividend rate of preferred shares is lower than the required rate of return, the value of the shares will be below par value.

In this case, as the maturity of the preferred shares increases from 10 years to 15 years, it extends the period over which investors will receive dividends at a rate lower than the required return. This longer period of receiving lower-than-required returns decreases the present value of future cash flows associated with the preferred shares.