How to use and interpret a perpetuity valuation
What this calculator estimates
A perpetuity is a stream of payments that is modeled as continuing without a final date. The calculator converts that infinite stream into one present-value estimate by discounting distant payments more heavily than near-term payments. A level perpetuity keeps the payment constant. A growing perpetuity changes the payment by the same percentage each period.
The default example uses a $10.00 next-period payment, an 8.00% discount rate, and 2.00% perpetual growth. The resulting $166.67 value follows the growing-perpetuity formula. Setting growth to zero produces the level-perpetuity value of $125.00.
Field-by-field guidance
- Solve for selects the unknown. Present value is the usual choice, but the reverse modes can infer the payment, discount rate, or growth rate when the other three quantities are known.
- Payment per period is the cash flow expected one period from now. Use annual dollars with annual rates, monthly dollars with monthly rates, and so on. A higher payment increases value proportionally.
- Discount rate represents the required return or opportunity cost for the same period. A higher rate reduces present value because future cash flows are discounted more aggressively.
- Growth rate is the constant percentage change in future payments. Higher growth increases value, but the standard model requires growth to remain below the discount rate.
- Present value is the current lump-sum equivalent. In reverse-solving modes, enter the observed price or target value here.
How the formulas work
For a level perpetuity, present value equals the next payment divided by the discount rate: PV = Payment ÷ r. For a growing perpetuity, the growth rate is subtracted from the discount rate: PV = Payment ÷ (r − g). Rates are converted from percentages into decimals before calculation.
The reverse modes rearrange the same relationship. Payment equals present value multiplied by the rate spread. Discount rate equals payment divided by present value, plus growth. Growth rate equals discount rate minus payment divided by present value. These rearrangements are useful for checking an implied return or implied perpetual growth assumption.
Understanding the results
The primary result is the variable selected in “Solve for.” The rate spread is discount rate minus growth rate, the denominator that controls valuation sensitivity. The payment yield is payment divided by present value; in a valid growing perpetuity it equals the rate spread. The level-perpetuity value shows the value with growth set to zero. The growth uplift is the difference between the growing and level values.
A zero payment gives a zero value when the rates are otherwise valid. A zero or negative discount rate cannot support the standard level-perpetuity formula. If growth equals or exceeds the discount rate, the infinite series does not converge to a finite value, so the calculator displays a validation message instead of an extreme or misleading number.
Reading the chart and table
The sensitivity chart varies only the discount rate. The blue series shows the value with the entered growth rate; the teal series shows the same payment with zero growth. The table exposes the exact values behind every plotted point. The row labeled “Current” corresponds to the assumptions entered above.
A steep curve signals that small changes in the discount rate materially affect value. This usually occurs when the discount rate and growth rate are close together. Use a wider set of plausible assumptions rather than relying on one precise estimate.
Practical inputs and common mistakes
Discount rates should reflect timing, risk, and the type of cash flow. Market reference rates can provide context, but they are not automatically appropriate for a specific security or project. The Federal Reserve’s 10-year Treasury series is one public benchmark, while the U.S. Bureau of Labor Statistics CPI resources provide inflation context.
Do not mix a current payment with a formula that expects the next payment. Do not combine monthly cash flow with annual rates. Avoid assuming a growth rate that can remain above long-run economic growth indefinitely. For a deeper treatment of dividend valuation conventions, see the CFA Institute’s discounted dividend valuation reading. The SEC Investor.gov compound interest calculator is also useful for reviewing how compounding changes future cash flows.
Benefits and limitations
The perpetuity model is transparent, fast, and useful for preferred shares, stabilized income streams, endowment-style spending, and terminal-value analysis. It makes the relationship between payment, required return, and growth explicit. It is also easy to audit because every result comes from a compact formula.
Its simplicity is the main limitation. Real cash flows can be interrupted, grow at different rates, face taxes or reinvestment needs, and carry changing risk. Many assets should be modeled with an explicit forecast period followed by a stable terminal stage. Treat this calculator as an analytical framework, not personalized investment, tax, or legal advice.
Using the Excel export
Download Excel creates a current-state workbook with Summary, Inputs, Breakdown, Sensitivity, and Notes sheets. It stores rates as true percentage values and money as numeric currency cells, so the workbook remains useful for review and documentation. Change an assumption before downloading and the exported workbook will reflect the updated model, including the reverse-solved variable and every sensitivity row.