perpetuity
Perpetuity is a stream of money that keeps paying forever, with no end date, and its worth today is simply the yearly amount divided by the rate of return.
In plain English
Mama Nkechi sells fabric at Balogun market, and every December she puts a little money in a cooperative that pays her a fixed amount every single year, for as long as she lives and, she jokes, even after, because she has told her daughter to keep collecting it in her name through the family trust.
What Mama Nkechi has stumbled into, without needing the textbook word for it, is the idea of a perpetuity. It is a promise of payment that never stops. Not five years, not twenty, forever, or as close to forever as anything gets in this life.
Finance people love perpetuities because some real things behave like them. A share that pays a steady dividend year after year with no planned end is often valued using this idea. Even certain government bonds in the United Kingdom, called consols, were structured to pay interest forever with no fixed date to return the original sum.
The maths is refreshingly simple. If something pays you a fixed amount every year forever, its value today is just that yearly amount divided by the rate of return you could get elsewhere. No long spreadsheet, no twenty rows of numbers, just one clean division.
Someone in London sending money home might think of it this way. If you promised your mother ₦300,000 every year forever, and money elsewhere earns 10 percent yearly, that promise is worth about ₦3,000,000 today. That is the whole trick of perpetuity, turning a never ending stream into one honest number you can hold in your hand right now.
If a company pays a steady dividend of ₦50,000 a year forever, and the required rate of return is 10 percent, the perpetuity is worth ₦50,000 divided by 0.10, which comes to ₦500,000 today.
Questions people ask
Does anything actually pay forever in real life?
Not truly forever, since companies close and governments change policies, but some things come close enough, like certain long standing preference shares or old UK consol bonds, so the perpetuity formula gives a useful estimate even when forever is really just a very long time.
How is a perpetuity different from an annuity?
An annuity pays a fixed amount for a set number of years and then stops, like a five year savings plan, while a perpetuity has no stopping point at all, it simply keeps paying, which is why its formula is shorter and simpler than an annuity's.
Why would an investor care about this formula?
It gives a quick, honest way to value shares that pay steady dividends, or to judge whether a cooperative or family arrangement that promises endless yearly payments is actually priced fairly today.
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