Calculator inputs
Example data table
| Scenario | Next Payment | Discount Rate | Growth Rate | Frequency | Timing | Estimated Value |
|---|---|---|---|---|---|---|
| Scholarship endowment | $1,200.00 | 9.00% | 3.00% | Annual | Ordinary | $20,000.00 |
| Subscription royalty stream | $2,400.00 | 12.00% | 4.00% | Annual | Ordinary | $30,000.00 |
| Immediate maintenance reserve | $2,500.00 | 10.00% | 5.00% | Annual | Due | $52,380.95 |
Formula used
1) Convert annual assumptions
Effective annual discount: r_eff = (1 + r_nom / m_r)^m_r - 1
Effective annual growth: g_eff = (1 + g_nom / m_g)^m_g - 1
Per-payment rates: i = (1 + r_eff)^(1 / f) - 1 and g = (1 + g_eff)^(1 / f) - 1
2) Ordinary growing perpetuity
PV = C1 / (i - g), where C1 is the next payment one period from now and i > g.
3) Growing perpetuity due
Current payment: C0 = C1 / (1 + g)
Total value: PV_due = C0 + C1 / (i - g)
This design lets the page handle annual, monthly, quarterly, or weekly assumptions in one consistent valuation workflow.
How to use this calculator
- Enter the next payment amount expected one payment period from now.
- Provide annual discount and growth assumptions as percentages.
- Select the number of payments received each year.
- Choose compounding settings for the discount and growth rates.
- Pick ordinary or due timing, depending on when cash starts.
- Set how many periods you want shown in the chart and table.
- Press the calculate button to display value, sensitivity, and exports.
- Use the CSV and PDF buttons to save the output.
Frequently asked questions
1) What is a growing perpetuity?
A growing perpetuity is an infinite stream of cash flows that rises by a constant rate each period. This calculator estimates its present value using your discount rate, growth rate, timing choice, and payment frequency.
2) When does the formula work best?
It works when growth is expected to remain stable for a very long time and the discount rate is higher than the growth rate. It is commonly used for valuation models, endowment estimates, and terminal value analysis.
3) Why must the discount rate exceed the growth rate?
If growth equals or exceeds the discount rate, the series does not converge to a finite value. In practical terms, the model would imply an unrealistic or undefined present value.
4) What is the difference between ordinary and due timing?
Ordinary timing assumes the first payment arrives one period from now. Due timing assumes a payment is received today, so total present value is higher.
5) Why does the calculator convert rates?
Nominal annual rates and payment schedules can differ. Converting them into effective annual and per-payment rates makes the valuation internally consistent before the perpetuity formula is applied.
6) Can I use monthly or quarterly cash flows?
Yes. Choose the payment frequency that matches your cash flow timing. The calculator converts annual assumptions into compatible per-payment rates automatically.
7) What does the sensitivity table show?
It shows how present value changes when discount and growth assumptions move around your base case. This helps you see upside, downside, and model fragility quickly.
8) Does the chart represent the whole perpetuity?
The chart visualizes the first projected payments, not infinity itself. The total value still includes the mathematical tail beyond the displayed periods through the perpetuity formula.