What Is a Perpetual Preferred Stock?

Perpetual annuities are special annuities that are collected and paid indefinitely. It is a special form of ordinary annuity. Because it is a series of cash flows with no end time, there is no final value, only the present value. Dividends of preferred stocks in real life, interest generated by the unified government bonds issued by the British government, some intangible assets that can be permanently used (such as goodwill), etc. belong to this. Its present value is: the amount of cash flow paid in each period and The ratio of returns required by investors. ^[1]

Perpetual annuity

Since the perpetual annuity has an infinite duration, there is no termination time, so there is no

If the following conditions are met:

1. The amount of each payment is the same and is A (Amount of Payment)

2. The payment cycle (time interval of each payment) is the same (such as: year, quarter, month, etc.)

3. The interest rate of each payment interval is the same and both are i (Interest Rate, according to different periods, it can be annual interest rate, monthly interest rate, etc.)

The present value (PV) calculation formula of the perpetual annuity is:

a. If the period-end payment for each period, PV = A / i

b. If the beginning of each period is paid, PV = A + A / i

Example: Someone sets up a charity fund in a university. The principal does not buy long-term government bonds with an annual interest rate of 5%, and the interest at the end of each year is 100,000 for scholarships for students. The principal required for this fund is P = 100,000 / 5% = 2 million, which is also the present value of the perpetual annuity.

If payment is required at the beginning of the period, the present value of the annuity P = A + A / i = 2 million + 100,000 = 2.1 million.