Growing perpetuity factor

Financial maths.

(GPF).

A growing perpetuity factor is the fraction 1/(r-g), used when evaluating a growing perpetuity.

Using this simple formula assumes a constant periodic cost of capital (r) for all periods from now to infinity.

It also assumes a constant compound rate of growth (g) from the first cashflow to infinity.

The formula can only be used when (r) is greater than (g).

Sometimes known as the Growing perpetuity formula.

(Q)

"I noticed that when the Growth Rate exceeds the Rate of Return, the NPV returns a negative value.

"Logically, one might think that having cash flows growing at a rate greater than the rate of return of return is a good thing and would therefore not result in negative present value. Is there any enhanced model that caters for this or did I get it wrong?"

(A)

"You've applied the formula correctly.

"The negative result, I'd classify as "not meaningful".

.

"The formula only works correctly when the Growth Rate is lower than the Rate of Return.

"The approach to get an answer when the Growth Rate is higher than this, for a LIMITED NUMBER OF PERIODS, is to:

- Forecast this "supernormal growth" period cash flow by cash flow individually;

- Sum the individual Present Values;

- Use the formula only when the Growth Rate has fallen, in a future period, to a constant lower figure;

- This will then be a modified form of the formula, for example: Time 5 value = Time 6 cash flow / (r-g)

- The resulting Time 5 value, for example, then needs to be discounted to a Time 0 value for comparability."

See also

• Annuity factor
• Compound
• Cost of capital
• Discounted cash flow
• Dividend growth model
• Growing annuity factor
• Growing perpetuity
• Perpetuity
• Perpetuity factor