When Does Perpetuity Decrease?

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A perpetuity is a fundamental concept in financial theory. Perpetuities represent annuities with cash flow that could be constant or growing. Three factors influence their valuation: the amount of the cash flow, the discount rate and the growth rate, if applicable.

What It Is

A perpetuity represents an infinite cash flow stream that makes payments at regular intervals. Constant perpetuities pay the same amount each period whereas growing perpetuities pay increasing amounts each period. Consol bonds issued by the British government and dividends from corporations with constant, reliable payment schedules can be treated as perpetuities.

Perpetuity Formula

The formula to assess the value of a constant perpetuity is to take the cash flow for one year and divide it by the discount rate. To assess the value of a growing perpetuity, the cash flow to be received in one year's time is divided by the discount rate minus the growth rate. The reduction in the denominator results in a higher value for the perpetuity to reflect its growth profile.

Example

Consider the example of a corporation that is expected to pay a \$100 annual dividend growing at a rate of 5 percent. Further assume that investors believe that a discount rate of 15 percent accurately reflects the risk of the company's cash flows. To assess the value of this growing perpetuity, divide the \$100 dividend by 10 percent (15 percent minus 5 percent), indicating a present value of \$1,000.

Factors that Decrease a Perpetuity's Value

As illustrated in the perpetuity formula, you have a maximum of three variables: the cash flow amount, the discount rate and, if applicable, the growth rate. A perpetuity will decrease in value if either the cash flow amount is reduced, the discount rate is increased, or the growth rate is reduced. Any of these factors individually or in combination will result in a decrease in the value of a perpetuity.

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