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If the annuity is expected to go on forever then it is called perpetuity and then the above formula reduces to:

                                                         

Perpetuities are not very common in financial decision-making as no project is expected to last forever but there could be a few instances where the returns are expected to be for a long indeterminable period. Especially when calculating the cost of equity perpetuity concept is very useful.

 

For a growing perpetuity the formula changes to:

                                               

All these calculations take into consideration that the cash flow is coming at the end of the period.