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Put a value on preferred stock that is neither callable nor convertible

CFA® Level I · Equities · Discounted Cash Flow (DCF) and Growth Models · EQ.12.b

The idea

A non-callable, non-convertible perpetual preferred share pays a fixed dividend forever, so it is valued as a perpetuity: V0 = D / r. A share paying 6 per year where investors require 8% is worth 75. Because the dividend does not grow, value moves inversely with the required return, much like a bond. A preferred with a fixed redemption date is valued like a bond instead, as the present value of the dividends plus the redemption amount. Contingency features change the value. A call option belongs to the issuer, so it lowers value and caps the price near the call price when rates fall. A put (retraction) option or conversion right belongs to the holder, so it raises value. A cumulative feature, which requires missed dividends to be paid before common dividends, also adds value.

Formulas

Non-callable, non-convertible preferred stock

V₀ = D ÷ r

V₀
the value of the preferred share
D
the level dividend paid each year
r
the return investors require on this preferred

A perpetuity: a fixed dividend forever. The required return is usually lower than the common's.

A practice question

From the question bank, with the reason each wrong option is wrong.

A non-callable, non-convertible perpetual preferred share pays an annual dividend of 6 and investors require 8%. Its value is:

  1. 75.00 - correct
  2. 100.00Why not: Assuming the share is worth its par value. That holds only when the required return equals the dividend rate.
  3. 133.33Why not: Dividing the required return by the dividend rate, 8 / 0.06, which inverts the perpetuity formula.

V0 = D / r = 6 / 0.08 = 75.00. The dividend does not grow, so the share is valued as a level perpetuity.

A harder one

Compared with an otherwise identical non-callable preferred share, a preferred share that the issuer can call at par is worth:

  1. moreWhy not: That is the effect of a feature held by the investor, such as a put. A call option belongs to the issuer.
  2. less - correct
  3. the sameWhy not: The call has value to the issuer, who will use it when that suits it, so it must lower the value to the holder.

The issuer will call the share when rates fall and the share would otherwise rise in value, so the holder gives up that upside. Investors pay less, or demand a higher yield, for callable preferreds.

The hardest tier

A preferred share with a par value of 100 pays an annual dividend of 7 and must be redeemed at par in five years. Investors require 9%. Its value is closest to:

  1. 77.78Why not: Valuing it as a perpetuity, 7 / 0.09. The fixed redemption date means it is valued like a bond.
  2. 100.00Why not: Using par value, which would be right only if the required return equalled the 7% dividend rate.
  3. 92.22 - correct

Value = PV of five dividends of 7 plus PV of 100 at 9%: 27.23 + 64.99 = 92.22.

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