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The present value of a growing annuity can be estimated in all cases, but one - where the growth rate is equal to the discount rate. In that case, the present value is equal to the nominal sums of the annuities over the period, without the growth effect.

PV of a Growing Annuity for n years (when r=g) = n A Note also that this formulation works even when the growth rate is greater than the discount rate.1

To illustrate a growing annuity, suppose you have the rights to a gold mine for the next 20 years, over which period you plan to extract 5,000 ounces of gold every year. The current price per ounce is $300, but it is expected to increase 3% a year. The appropriate discount rate is 10%. The present value of the gold that will be extracted from this mine can be estimated as follows:

1 Both the denominator and the numerator in the formula will be negative, yielding a positive present value.

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