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# 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

Dt = 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

Since the required rate of return as of the valuation date is higher than the dividend yield (as a % of par value) of ABC’s preferred shares, the current valuation of ABC’s preferred shares declines as maturity increases.

If ABC’s preferred shares instead yielded 9%, their current value would move in the same direction as maturity.

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