Perpetuities

We've seen that a series of level cash flows can be valued by treating those cash flows as an annuity. An important special case of an annuity arises when the level stream of cash flows continues forever. Such an asset is called a perpetuity because the cash flows are perpetual. Perpetuities are also called consols, particularly in Canada and the United Kingdom. See Example 6.7 for an important example of a perpetuity.

Because a perpetuity has an infinite number of cash flows, we obviously can't compute its value by discounting each one. Fortunately, valuing a perpetuity turns out to be the easiest possible case. The present value of a perpetuity is simply:

For example, an investment offers a perpetual cash flow of $500 every year. The return you require on such an investment is 8 percent. What is the value of this investment? The value of this perpetuity is:

This concludes our discussion of valuing investments with multiple cash flows. For future reference, Table 6.2 contains a summary of the annuity and perpetuity basic calculations we described. By now, you probably think that you'll just use online calculators to handle annuity problems. Before you do, see our nearby Work the Web box!

Ross et al.: Fundamentals I III. Valuation of Future I 6. Discounted Cash Flow of Corporate Finance, Sixth Cash Flows Valuation

Edition, Alternate Edition

Time value applications abound on the Web. See, for example, www.collegeboard.com, www.lstmortgagedirectory. com, and personal.fidelity.com.

perpetuity

An annuity in which the cash flows continue forever.

consol

A type of perpetuity.

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