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Show why the formulae for growing perpetuity holds only when r>g

Show why the formulae for growing perpetuity holds only when r>g

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Answer #1

We know that, growing for present value of a growing perpetuity is

Price = next year dividend /(Required rate of return r - growing rate g).

This formula only holds when r>g, so that denominator is positive. If growing rate goes above the required rate of return, the present value of series will be a growing series and sum of a growing series can not be determined. If r = g, then denominator of the formula is 0, that makes the formula invalid.

That's why r should always be greater than g in a growing perpetuity to use the present value formula.

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