perpetuitydue

Perpetuity due is a type of perpetuity in finance in which the payments occur at the beginning of each period, as opposed to ordinary perpetuity where payments are made at the end of each period. The cash flows, equal in size, are assumed to continue indefinitely.

Formula: If each payment is PMT and the periodic discount rate is r, the present value of a perpetuity due is PV = PMT × (1 + r) / r. For an ordinary perpetuity with end-of-period payments, the present value is PV = PMT / r.

Example: If PMT = 100 and r = 5%, PV of a perpetuity due is 100 × 1.05 / 0.05 = 2,100; the PV of the corresponding ordinary perpetuity would be 100 / 0.05 = 2,000.

Implications: The perpetuity due is worth more than the ordinary perpetuity by a factor of (1 + r), reflecting the immediate receipt of the first payment.

Applications and limitations: The concept is used in theoretical valuation models and for cash flows assumed to start immediately and continue indefinitely, such as some dividend models. Real-world cash flows typically are not truly perpetual and may grow, decline, or terminate; the model is sensitive to the discount rate and the payment size.

See also: ordinary perpetuity; annuity due; perpetual growth model.