The Magic of Growth Multipliers
The magic by which seemingly small income streams get magnified into huge market valuations is intimately tied up with the arcane mathematics of perpetuities. It sounds dull, but it is well worth understanding because it is the mathematical foundation of Wall Street wealth.
Aperpetuity is defined as an investment offering a level stream of cash flows forever. What is the value of a perpetuity paying $100 per year forever? Using a cost of capital of 12 percent, it would be the present value of the first payment, plus the second payment, plus the third payment, . . . , plus the fiftieth payment, and so on; that is, $89.29 + $79.72 + $71.18 . . . . The value of the payments gets progressively smaller. The value of the fiftieth payment is only 3 cents!
It turns out that the present value of this stream, no matter how far one goes out in time, cannot exceed $833.33. That number is the free cash flow of $100 divided by the cost of capital, 12 percent, or 0.12—a very simple relationship that we introduced earlier.
Mathematicians say simply that this series converges to a finite limit. This one converges fairly quickly—it reaches 90 percent of the limit in 20 years, and 95 percent in 26 years. So in a practical sense, realizing the value of a perpetuity does not take forever, just a period of time that is consistent with the lifetime of a durable business.