perpetuity calculator - Aaron Graves, PhDude Replica

Perpetuity Value Calculator

Use this tool to calculate either the present value of a perpetuity or the cash flow a principal amount can sustain forever.

Calculation mode

Cash flow next period ($)

For a level perpetuity, this is the constant payment each period.

Principal / Present value ($)

Enter the amount invested today.

Discount rate r (% per period)

Growth rate g (% per period, optional)

Set to 0 for a level perpetuity. For a growing perpetuity, r must be greater than g.

What Is a Perpetuity?

A perpetuity is a stream of cash flows that continues forever. In finance, it is a useful model for assets or policies where payments are expected to continue indefinitely, such as certain preferred stocks, endowments, or long-term spending plans.

The core idea is simple: if you know the cash flow and the discount rate, you can estimate the value today. This is exactly what a perpetuity calculator does.

Perpetuity Formulas

1) Level Perpetuity

When payments never change:

PV = C / r

PV = present value today
C = cash flow received each period (starting next period)
r = discount rate per period (as a decimal)

2) Growing Perpetuity

When payments grow at a constant rate forever:

PV = C₁ / (r - g)

C₁ = cash flow in the next period
g = growth rate per period
Requirement: r > g

How to Use This Perpetuity Calculator

To find present value

Select Present Value from Cash Flow.
Enter the next period cash flow.
Enter discount rate and optional growth rate.
Click Calculate.

To find sustainable cash flow

Select Cash Flow from Principal.
Enter principal amount, discount rate, and growth rate.
Click Calculate to estimate cash flow that can continue indefinitely.

Example Scenarios

Example A: Level Income

If you need $4,000 per year forever and your discount rate is 5%, then:

PV = 4,000 / 0.05 = $80,000

You would need $80,000 today under these assumptions.

Example B: Growing Income

If next year's cash flow is $4,000, growth is 2%, and discount rate is 6%:

PV = 4,000 / (0.06 - 0.02) = $100,000

Growth increases the present value because future payments rise over time.

Common Mistakes to Avoid

Mixing annual and monthly rates/payments.
Using a discount rate that is less than or equal to growth rate in a growing perpetuity.
Forgetting that cash flow in the formula is typically the next period amount, not today's amount.
Ignoring risk: higher uncertainty usually means a higher discount rate.

When a Perpetuity Model Is Useful

Perpetuity math is especially helpful for quick valuation estimates, retirement drawdown planning, scholarship funds, and long-horizon policy analysis. Real life is never truly infinite, but perpetuity formulas provide a clean approximation for very long-lived cash flows.

Final Thoughts

This perpetuity calculator is best used as a decision support tool. Adjust your discount rate and growth assumptions to run optimistic and conservative cases. Small changes in rates can produce large differences in estimated value, so scenario testing is essential.