What is the growing perpetuity formula?

PV = P1 ÷ (r − g), where P1 is the first payment (one period from now), r the discount rate and g the constant growth rate, with r greater than g.

What happens if g is greater than r?

The formula no longer applies: the payments grow faster than they are discounted and the present value is infinite.

Should I use the current payment or next period's payment?

Next period's payment, P1. If you know the payment just made, multiply it by (1 + g) first.

How is this used in stock valuation?

With dividends as the payments it becomes the Gordon growth model, P0 = D1 ÷ (r − g).

Growing Perpetuity Formula

Home › Finance Formulas › Growing Perpetuity Formula

Growing Perpetuity Calculator

A growing perpetuity is a stream of payments that continues forever and grows at a constant rate g each period. The first payment, P₁, arrives one period from now, the next is P₁(1 + g), then P₁(1 + g)², and so on. As long as the discount rate r is larger than g, the discounted payments shrink over time and the total converges to P₁ ÷ (r − g).

Formula

PV = P₁r − g (r > g)

Where

PV: present value of the growing payment stream
P₁: first payment, received one period from now
r: discount rate per period
g: growth rate of the payment per period

Calculator

First payment (P₁)

Discount rate (r) (%)

Growth rate (g) (%)

Result and step-by-step solution

Present value of the growing perpetuity

20,000.00

First payment 1,000.00, growing 3% a period, discounted at 8%.

Convert the rates
r = 0.08, g = 0.03
Spread between discount and growth rate
r − g = 0.08 − 0.03 = 0.05
Divide
PV = 1,000.000.05 = 20,000.00

How to use the formula

This short formula is one of the most used in finance. It values a stock whose dividend grows steadily (the Gordon growth model), gives the terminal value at the end of a discounted cash flow forecast, and prices rental income that rises with inflation. The result is very sensitive to the spread r − g: in the example, a first payment of 1,000 with r = 8% and g = 3% is worth 20,000, but if g rises to 4% the value jumps to 25,000.

The formula fails when g is equal to or above r, because the payments would grow faster than they are discounted. For a stream that stops after n payments, use the present value of a growing annuity.

Frequently asked questions

What is the growing perpetuity formula?: PV = P₁ ÷ (r − g), where P₁ is the first payment (one period from now), r the discount rate and g the constant growth rate, with r greater than g.
What happens if g is greater than r?: The formula no longer applies: the payments grow faster than they are discounted and the present value is infinite.
Should I use the current payment or next period’s payment?: Next period’s payment, P₁. If you know the payment just made, multiply it by (1 + g) first.
How is this used in stock valuation?: With dividends as the payments it becomes the Gordon growth model, P₀ = D₁ ÷ (r − g).

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.