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The term perpetuity is largely defined as something that goes on infinitely, but in investing and corporate finance circles, perpetuity takes that "eternal" concept and adds a dollar sign to it.

Understanding perpetuity can help not only senior corporate financial decision-makers to better understand the flow of money, but it can also help Main Street Americans - in a limited fashion - improve their financial standing by applying perpetuity to their own long-term money goals.

Let's take a look at perpetuity and see how it applies to various financial levels.

What Is Perpetuity?

Perpetuity is widely used by companies to properly place a value on various investments, such as stocks, bonds, real estate and especially annuities.

With perpetuity, payments from these investments theoretically never stop, making perpetuity a stream of cash flow that has no end limit. An individual or a firm that buys a perpetuity-based investment expects payments to go on infinitely, usually after making a lump sum payment or a series of payments over time, in return for a perpetual cash stream in return.

Consider an investor who purchases a stock that pays generous dividends. After evaluating the stock, and deciding that the dividend is too good to pass up, the investor buys the stock with the security that the company will pay out dividends to its shareholders in perpetuity - or forever.

The same goes with the concept of perpetuity and real estate. If an investor buys a property he or she plans to rent out to people, that investor believes he or she will earn rental perpetuities in perpetuity forever - as long as that investor owns the property.

Are Annuities a Form of Perpetuity?

Perhaps the most obvious - and seemingly easiest - examples of perpetuity in action are annuities, which in some ways are modeled upon the perpetuity premise of steady streams of cash flow that have no end.

Annuities are widely used in the retirement planning realm, where savers make an up-front or series of upfront payments to an insurance company. In return, the money is invested and sent back to the annuitant in retirement, via a series of regular payments that are made in perpetuity.

Yet annuities aren't technically a form of perpetuity, even though the two do share common characteristics. In fact, there are sharp variances between perpetuity and annuities, as follows:

  • Structurally, perpetuity is shaped in an annuity mold, but annuities aren't perpetuity.
  • By definition, an annuity represents cash flow of a fixed payment, for every payment, over a specific period of time (like 20 years for a retiree.) Perpetuity is different, as payments are made on a "forever" basis.
  • Annuities also represent a two-way investment - an annuity can be given and an annuity can also be received. Perpetuity, however, only ones goes one way, via cash flow from a single entity to another entity.
  • Annuities are calculated differently than perpetuity, as well. Annuities, after all, allow for fairly basic calculations based on a formula that prioritizes projected growth over a specific period of time. Since perpetuity is endless, that type of formula can't be used.

Is Perpetuity Really Forever?

An obvious question with perpetuity is this - can cash stream payouts really go on forever? Technically, yes, but there is a huge caveat.

While perpetuity does allow for the payment of money with no end in sight, that cash payout diminishes on a gradual, year-by-year basis as inflation chews into the value of those fixed payouts. Thus, the real value assigned to cash streams made in perpetuity does decline over time - especially endless time.

There is a form of perpetuity that fuels ongoing growth in asset payments made over time. That's called a growing perpetuity. Here, instead of garnering steady, fixed payments in perpetuity, the recipient gets a regular stream of payments that grow steadily.

That way, a growing perpetuity payment with a growth rate of 7% will have each future payment amount be higher by 7%.

As the real value of perpetuity cash streams declines over time, it's also worth noting that the present value of those regular cash payments is highest in the early years, even though the payout is fixed.

As inflation eats away at the value of the payments, that value deteriorates. That's why the cash flows - way down the road - wither down to almost nothing, but technically never to a zero amount.

What's the Formula for Perpetuity?

Perpetuity offers several different formulas, but a foundational calculation is dividing cash flows by various discount rates, which is the interest rate financial institutions pay to borrow cash from the Federal Reserve.

This gives a business the value of its cash flow, an important slice of data as it aids in determining the firm's total cash flow in a single year.

This calculation figures the present value of a growing perpetuity, and is actually a simple formula, only requiring four factors:

  • The present value model. There are just two models to choose from - a growing perpetuity, where the cash stream grows over time, and perpetuity, which delivers cash flow that goes on forever, but with a fixed payment.
  • The cash flow amount. The amount of money generated by a specific investment (an annuity is a good example). When the cash flow amount is calculated for a growing perpetuity, it is represented as the beginning value of that cash flow.
  • The discount rate. The rate at which future cash flows are discounted to a growing value. If the future value is to be discounted by 5% over a specific period of time, that means the discount rate is 5%.
  • The expected growth rate. The growth rate of expected future cash flows, on an annual basis. For instance, a $500 cash flow in the first year of the perpetuity, with an expected growth rate of 10%, would amount to a $550 payment in year number two. This is used only for growing perpetuity.
  • Present value of cash flow. The current value of an asset or an investment, relative to the time value of money. In this calculation, the value discounts the cash flow dollar amount by the designated interest rate.

Consequently, the correct calculation in valuing perpetuity is short and direct:

PV = C / R

Where:

  • PV is the present value of perpetuity
  • C is the amount of cash flow received every period
  • R is the required rate of return

Forever Payments, Declining Value

The takeaway on perpetuity? Think of it as a cash stream that is paid out endlessly, but does deteriorate in value over a long period of time thanks to inflation.

It's an economic concept worth getting to know, to get a better handle on the value of cash flow over time - a lot of time.