Perpetuity

4 formulas

Perpetuity formulas value infinite payment streams that continue forever. While no payment truly lasts forever, perpetuities are used to value preferred stock dividends, endowments, and any cash flow expected to continue indefinitely. The math simplifies elegantly because the present value converges to a finite number.

Constant Perpetuity

PV of Perpetuity

Present value of an infinite stream of equal end-of-period payments.

PV = \frac{PMT}{k}

Showing annual compounding

3 compounding options

PV of Perpetuity Due

Present value of infinite payments made at the beginning of each period.

PV = PMT + \frac{PMT}{k}

Showing annual compounding

3 compounding options

Growing Perpetuity

PV of Growing Perpetuity

Present value of an infinite stream of payments growing at rate g forever (Gordon Growth Model).

PV = \frac{PMT}{k - g}

PV of Growing Perpetuity Due

Present value of an infinite growing stream with payments at the beginning of each period.

PV = \frac{PMT \times (1 + k)}{k - g}