Growing Perpetuity

A growing perpetuity is a theoretical concept, since nothing truly lasts forever, but it is extremely useful in valuation. Its present value has a simple solution: the first cash flow divided by the difference between the discount rate and the growth rate.

For example, if an investment will pay 100 next year, growing by 3% a year forever, and the appropriate discount rate is 8%, its present value is 100 divided by 5%, or 2,000.

The growing perpetuity is the basis of the Gordon growth model, which values shares as a stream of dividends growing at a constant rate. It is also used to calculate the terminal value in a discounted cash flow model, representing the value of all cash flows beyond the forecast period.

The formula only works when the growth rate is lower than the discount rate. Results are very sensitive to both inputs. In the example above, raising the growth rate from 3% to 4% increases the value from 2,000 to 2,500. For this reason, analysts usually use conservative long-term growth rates, often close to expected inflation or long-term economic growth.