In the world of finance and investment we hear many terms, but do we truly know what they mean?

Perpetuity is one of them. This article aims to clarify what this term means, and what place it has in the world of finance and investment.


Definition of Perpetuity

Definition of Perpetuity

The definition of perpetuity is not limited to the world of business and finance. In its general meaning, the term perpetuity means: the state or quality of lasting forever.

When it comes to it’s application in finance, it has a much more specific meaning. In this context it means: a continual stream of equal cash flows which have no end.  While the cash flows are infinite, the present value of a perpetuity can still be determined.

The following formula is used to calculate the present value of a perpetuity:

PV = c/r

Pv = present value

c = coupon or payment amount

r = interest rate



Perpetuity Explanation

Many people are aware of or own annuities. These are streams of cash flow, and perpetuity refers to a type of annuity that is eternal. The cash maintains a continual stream that lasts forever.

Perpetuity is a concept that is relevant to many types of investments. The formula used for perpetuity allows financial analysts to attach value to things such as stocks, land, estates and investments.

The perpetuity calculation is often applied as a valuation methodology. It is used to find a company's present cash flow value in light of a fixed interest rate.

The calculation is used to ascertain the amount of future cash flows. In terms of valuation, the company would be classed as a going concern. This means it goes on forever.

Analysts apply a concept referred to as the terminal year, which is based on the company’s future value.


Finite Value

When it comes to a perpetuity, the full worth is infinite but the present worth is limited. To calculate the present worth of a stream of cash flow that is infinite there are steps to follow. You need to add up discounted values of each annuity plus the reduction of the discounted annuity worth.

This is done for each cycle until the values reach close to nothing.

Although it seems illogical, infinite series of cash flows also have finite present values. However, each payment is a fraction of the last due to the time value of money


Perpetuity in Use

A good example of financial agents that have perpetual cash flows are British bonds. These bonds are often known as consols, and are purchasable from the British government. The holder of the bond will receive an annual interest payment forever.

Another example is real estate. This becomes apparent when a buyer obtains a property and then chooses to rent it out. The buyer of the property will receive an infinite cash flow for as long as they own the property.

This is of course based on the assumption someone will rent it.

Preferred stock is also another example of perpetuity. The calculation of perpetuity assumes that the corporation will exist in the stock market indefinitely. It also expects that it will continue to pay out dividends.


Annuity or Perpetuity

Basically, a perpetuity is an annuity for which you will receive payments periodically on a fixed date. As we’ve explained, these payments will continue without an end date. They are sometimes referred to as a perpetual annuity.

We often see both words used together but that doesn’t mean they are actually the same things. Although annuities provides a constant cash flow like perpetuities, they do in fact differ.

If you have annuity you would receive payments for a specified period of time only. This could be for a year or multiple years, but there is a fixed end date to the payments.

As we have already seen this is not the case with perpetuity. These are indefinite payments.

There are some key differences between the two and the major ones are:

  • An annuity is a series of cash flows of equal amounts over a limited period, whereas, perpetuity continues indefinitely.
  • Payments are made or received for annuity, but with perpetuity there is only a cash outflow.
  • Future value of the annuity is calculable but for perpetuity, it is not.
  • All perpetuities are annuities, but most annuities are not perpetuities.


What Are Perpetual Bonds?

perpetuity

Sometimes a company or a government may decide to raise money. To do this they sell bonds which people can purchase. As a buyer, you are essentially providing the government or business with a loan.

In return for the money you loan them, you receive the bond. The company stipulates to make interest deposits to you for a certain period of time.

If the bond is a perpetual bond, then the period of time is indefinite. This means you will continue to receive interest payments forever.

Perpetual bonds operate similarly to stocks that pay dividends. Just as the stock owner receives a remittance as long as stock is owned, the same is true for the bondholder.

Perpetual bonds are not new; they have been in existence for many years. The British were thought to have created the first one, as early as 1694.

Perpetual bonds are not as popular as Treasury or municipal bonds, but to date they are still issued.



Benefits of Perpetual Bonds

Perpetual bonds are of interest to many people due to the fact that they offer sources of steady and predictable income.

Payments are received on a scheduled timetable and some also have a step up opportunity. This feature increases the payment at a future date that has been predetermined.

An example of this would be where a bond increases the yield by one percent after ten years. It could also offer a periodic interest rate increase.

Investors looking at buying perpetual bonds should pay close attention to step-up offers. This is one factor you should compare between bonds when choosing which ones to purchase. A growing perpetuity can be a good investment that will offer you more benefits in the future.


Risks With Perpetual Bonds

All investments incur some risks and perpetual bonds are no different. There are in fact  numerous risks associated with them. These risks are linked to the fact that perpetual equates to a long period of time.

As time goes by, the issuer, whether a government or a corporation, could encounter financial difficulty or even fail.

Another risk factor is call risk. This means the issuer may choose to recall the bond.

Other risks associated with perpetuity bonds are interest rates. Over time, general interest rates may rise. If there is a significant rise in rates, the rate paid from the bond might be lower than the current interest rate.

This means investors could make more money if they held a different type of bond based on current interest rates. But if they decide to go for a higher rate bond they would have to sell the perpetual one.

Such a sale could result in its value being less than the purchase price.  This is due to investors discounting their offers based on the interest rate differential.



Establishing the Value of a Bond

perpetuity

There is a simple calculation to use that will help determine the current value of a perpetual bond.

Current yield = (annual dollar interest paid x bond value) / 100%

As you can see that is a relatively easy calculation. Although it’s a complex concept, it’s not difficult to determine the current value of a perpetual bond.

In theory, perpetual bonds do not mature so payments will continue forever. But it is important to remember that, over time, money loses value. This is due in large part to inflation.

As time passes, the rate of interest paid to investors from the bonds has less value than it did initially. The discount rate reflects the pace at which money loses value over time.

For bonds that offer a growing perpetuity, there is another calculation used to determine present value. This one is a bit more complicated, and beyond the scope of this article. However there are easy to use online calculators that can do the work for you.

There are in fact many online resources to help with calculating values. If you are new to investing don’t let the calculations deter you from choosing the right ones for you. Utilizing the many resources that are available can help you make a more informed decision when purchasing these bonds.



Summary

Give yourself a pat on the back. You have just gained some valuable knowledge on potential investments. Perpetuity is a complicated concept. We have attempted to simplify it a bit so that you can make informed investment decisions.

Perpetuity has both pros and cons, like any other investments.

We have provided you with some of the clear advantages and disadvantages. We have also made you aware of some of the risks involved. With this knowledge, you can now decide if perpetuity is the right type of investment for you.