Perpetuity Calculator

What is a Perpetuity?

A perpetuity is a constant stream of identical cash flows that continues indefinitely with no end date. In financial valuation, calculating the present value of a perpetuity allows investors and financial analysts to determine the current worth of infinite future payment streams, such as preferred stock dividends, consol bonds, or perpetual annuities.

Perpetuity Valuation Formula

The present value of a standard (zero-growth) perpetuity is calculated using a straightforward formula:

$$PV = \frac{C}{r}$$

Where:

• $PV$ is the Present Value of the perpetuity stream.
• $C$ is the fixed periodic cash flow payment amount.
• $r$ is the discount rate or required rate of return per period.

Growing Perpetuity Formula

When the cash flow stream increases at a constant growth rate $g$ each period, the present value is calculated using the Gordon Growth Model variant:

$$PV = \frac{C}{r - g}$$

Where:

• $g$ is the constant annual growth rate of the cash flows (must be strictly less than the discount rate $r$).

Example Calculations

Standard Perpetuity: Suppose a preferred share pays an annual dividend of $100 forever, and your required discount rate is 5%. The present value is calculated as:

$$PV = \frac{\$100}{0.05} = \$2,000$$

Growing Perpetuity: If an asset pays $100 next year and cash flows grow at 2% annually with a 6% discount rate:

$$PV = \frac{\$100}{0.06 - 0.02} = \frac{\$100}{0.04} = \$2,500$$