A perpetuity is an annuity in which the constant periodic payments begin on a fixed date and continue indefinitely. It is sometimes referred to as a perpetual annuity. Examples include:
Despite its paradoxical infinitude, perpetuity analysis remains a remarkably practical cash flow planning technique. The value of the perpetuity is finite because receipts that are anticipated far in the future have extremely low present value (present value of the future cash flows). Unlike a typical bond, because the principal is never repaid, there is no present value for the principal. Assuming that payments begin at the end of the current period, the price of a perpetuity is simply the periodic payment (coupon amount) over the appropriate discount rate or yield; that is,
While true perpetual securities are less common nowadays, the concept enables several valuable analyses:
Perpetuity calculations help model the lifetime cash flow impacts of trusts, inheritance scenarios, and generational wealth transfers.
Rental properties, royalties, and other income sources can be valued as perpetuities to determine reasonable purchase prices or divestment values.
Monte Carlo simulations let us model maximum annual withdrawal rates from a portfolio that could theoretically continue in perpetuity.
Perpetuity math aids comparisons for life insurance covering dependents vs. invested lump sums generating equivalent perpetual incomes.
Understanding the value of perpetual sources and obligations clarifies impacts on long-term, multi-generational family cash flows.
While no income stream may truly last forever, framing certain financial decisions and assets through the lens of a perpetuity aids inter-generational planning. It quantifies the present value of perpetual income sources that could benefit multiple descendants.