## Summary of Special Cash Flow Stream Formulas

The growing annuity I am not a fan of memorization, but you must remember the growing perpetuity formula. (It formula — use is rare.

would likely be useful if you could also remember the annuity formula.) These formulas are used in many different contexts. There is also a growing annuity formula, which nobody remembers, but which you should know to look up if you need it. It is

It is sometimes used in the context of pension cash flows, which tend to grow for a fixed number of time periods and then stop. However, even then it is not a necessary device. It is often more convenient and flexible to just work with the cash flows themselves within a spreadsheet.

A summary Figure 3.1 summarizes the four special cash flow formulas. The present value of a growing perpetuity must decline (r > g), but if g > 0 declines at a rate that is slower than that of the simple perpetuity. The annuity stops after a fixed number of periods, here T = 7, which truncates both the cash flow stream and its present values.

Figure 3.1: The Four Payoff Streams and Their Present Values

Simple Perpetuity

Growing Perpetuity

Formula: PV

Formula: PV

Formula: PV

Formula: PV

Formula: PV

Formula: PV

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