Perpetuity Formula Explained: How to Calculate Perpetuity Value

A perpetuity is any form of investment that offers an annual payment to its holders forever (or in perpetuity). At least theoretically, financial modeling indicates investors can expect periodic payments for an infinite amount of time when they own a security of this ilk.

The time value of money allows certain preferred stocks, real estate investments, and companies to accrue money endlessly, allowing them to become perpetuities for interested and eager investors.

The perpetuity formula proceeds as follows: Present Value (PV) = Cash Flow (CF)/Interest Rate (IR). It acts as an innate perpetuity calculator capable of determining all present and future cash flows for investments of this type.

The perpetuity formula differs from an annuity formula in that there is no set maturity date for the investment—the perpetuity will keep yielding returns infinitely, whereas an annuity will cease providing these dividends at a certain point in the future.

To determine the present and future values of your perpetuities, you will need to calculate them using a premade formula. Follow these steps to figure out the infinite returns coming your way:

1. 1. Define your cash flow. Figure out the stream of cash flows you have coming in from a specific perpetuity investment. Suppose you own a preferred stock that pays out an annual dividend of a hundred dollars. This periodic payment will stand in for your cash flow (or CF) variable as 100. So far, the perpetuity formula should read: PV = 100/IR.
2. 2. Divide by the interest rate. Now imagine the compounding growth rate of return (or discount rate) on this stock is 5% a year. To represent this in the formula, you’ll convert the percentage into a decimal so your interest rate or IR variable stands as 0.05. The present value formula should now read PV = 100/0.05.
3. 3. Finalize the valuation of your perpetuity. As the final phase in your growing perpetuity formula, divide your CF by your IR to arrive at the present value of a perpetuity. In this example, that puts the current value at $2,000. The equation now reads accurately as 2,000 = 100/0.05. As you can see, the growth model for these sorts of infinitely returning investments allows for quite a high rate of growth.

The perpetuity formula is useful in various situations throughout the financial world. Here are three examples of where you might find using it handy:

1. 1. Consol bonds: The Bank of England used to offer consol bonds capable of generating an infinite series of cash flows over time. The British central bank phased out these perpetuities in favor of other more sustainable types of annuities in 2014. In other words, some perpetuities do stop providing dividends at a certain point even if those issuing them didn’t intend this at first.
2. 2. Preferred stocks: In comparison to common stock, preferred stocks often offer dividends on a more concrete schedule over an infinite period of time. So long as the investor holds on to these securities, they can expect to receive a cash flow in perpetuity (hence the name of the asset).
3. 3. Real estate investments: Once an owner puts up the cost of capital to buy a property, they can generate terminal value from it over an infinite amount of time. Rent payments operate as a type of perpetuity for landlords—as long as they provide upkeep and tenants continue to reside in their homes, the landlords can rely on a never-ending stream of extra income.

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