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Present Value of Growing Perpetuity Calculator

This Present Value of Growing Perpetuity Calculator helps you determine the present value of an infinite series of payments that grow at a constant rate over time.

Growing Perpetuity Present Value Estimator

Input Fields
C
$
Enter the amount of the annual payment or cash flow
r
%
Enter the annual interest rate
g
%
Enter the annual growth rate of the cash flow
If enabled, the result will update automatically when you change any value.

Present Value of Growing Perpetuity Formula

Formula
$$PV = \frac{C}{r – g}$$

Where:

  • $$PV$$ = Present value of the growing perpetuity
  • $$C$$ = Cash flow in the first period
  • $$r$$ = Discount rate (as decimal)
  • $$g$$ = Growth rate of the cash flows (as decimal)


Growing Perpetuity – Calculation Example

Suppose a company pays $200 annually in perpetuity, growing at 3% per year. If the discount rate is 7%, what is the present value?

Given:

  • $$C$$ = 200
  • $$r$$ = 0.07
  • $$𝑔$$ = 0.03

Calculation:

  1. $$PV = \frac{200}{0.07 – 0.03}$$
  2. $$PV = \frac{200}{0.04}$$
  3. $$PV = 5,000$$

The present value of the growing perpetuity is $5,000.

The Present Value of Growing Perpetuity Calculator is used to determine the value today of a stream of cash flows that grow indefinitely at a constant rate. This formula is commonly used in valuation of stocks (like the Gordon Growth Model), business models with infinite lifespans, and economic forecasting. It assumes that the growth rate is less than the discount rate, ensuring convergence.

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