Perpetuitet

Perpetuitet, in finance often called a perpetuity or perpetual annuity, is a stream of identical cash flows that continues forever. It represents the limiting case of an ordinary annuity as the number of payments grows without bound.

For a perpetuity with a fixed payment C each period and a periodic discount rate r, the present value depends on when the payments occur. If payments are made at the end of each period (perpetuity immediate), the present value is PV = C / r. If payments are made at the beginning of each period (perpetuity due), the present value is PV = C * (1 + r) / r.

A growing perpetuity allows payments to rise at a constant rate g each period, with r > g. If the first payment is C1 in the next period, the present value is PV = C1 / (r - g). This formula requires that the discount rate exceeds the growth rate.

Common applications include valuing perpetual cash flows such as preferred stock that pays a fixed dividend indefinitely, government consols, or certain long-term budgeting and capital-allocation models.

Limitations and assumptions should be noted. Perpetuities assume a constant payment forever and a constant discount rate, which may not hold in practice. They are sensitive to the chosen rate and can be less meaningful when cash flows or rates are expected to change over time.