Perpetuity Calculator

Perpetuity

A perpetuity is a series of cash flows that continue forever, with no end date. Despite paying forever it has a finite present value, because each payment is discounted harder than the one before it.

Simple Perpetuity:

PV = C / r

Growing Perpetuity (Gordon Growth Model):

PV = C / (r - g)

Where g is the constant growth rate of payments. Only valid when r > g.

The same formula handles a declining perpetuity: put in a negative g and the denominator widens, so the present value falls below the flat case. A royalty on a depleting well or a franchise losing 3% of its customers a year is exactly this. The flat formula C / r is just the special case where g happens to be zero.

Examples:

• British consol bonds pay a fixed coupon forever: classic perpetuity
• Preferred stock with fixed dividends is often modeled as a perpetuity
• Real estate held forever: net operating income / cap rate
• Terminal value in DCF models often uses the Gordon Growth Model

The power of the discount rate:

A small change in the discount rate moves the present value a long way. That is the whole reason interest rates hit long-duration assets so hard: at 2% the same thousand a year is worth five times what it is worth at 10%.

Why perpetuities matter: The Gordon Growth Model is used to value stable dividend-paying stocks:

P = D1 / (r - g)

Where D1 is next year’s dividend, r is required return, g is dividend growth rate.

Limitation: The model assumes constant growth forever, which is unrealistic for most businesses. Growth must be sustainable and below the discount rate. It works best for mature, stable dividend payers like utilities and consumer staples.