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

CFA® Level I · Equity Investments · 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.

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

A perpetual, non-callable preferred share pays an annual dividend of 5.40 and trades at 72. The required return implied by its price is:

  1. 5.4%Why not: The dividend rate on a par value of 100, which is not the return at a price of 72.
  2. 13.3%Why not: Dividing price by dividend, 72 / 5.40, which gives a multiple rather than a rate of return.
  3. 7.5% — correct

Rearranging V0 = D / r gives r = D / V0 = 5.40 / 72 = 7.5%.

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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