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Finance · level 1

Perpetuity and Gordon growth

A stream forever is one division. Growth simply shrinks the denominator — and because it shrinks it, small changes in g swing the value enormously.

Theory: Time Value of Money

Worked example: $10M a year growing 3%, discounted at 10%. Value today?

cash flow$10M
r − g7%
value$142.86M
implied multiple14.3×

Step by step

  1. 1

    Gordon growth

    V = CF / (r − g)

  2. 2

    Denominator

    10% − 3% = 7%

  3. 3

    Divide

    $10M / 0.07 = $142.86M

  4. 4

    Read it as a multiple

    14.3× the cash flow

$10M a year growing 3%, discounted at 10%. Value today? = 142,857,143

The theory behind it

Intuition

CF / (r − g) is the sum of an infinite geometric series. The gap between r and g is doing all the work: halve the gap and you double the value.

Common pitfalls

  • ×Setting g above or near r, which gives a nonsense or explosive value.
  • ×Using next year's flow when the formula needs the flow one period after the valuation date.

In the interview

Terminal value in a DCF, and the value of a stable annuity-like business.