Growing Perpetuity Calculator

A growing perpetuity is a series of cash flows that continues indefinitely, with each payment increasing at a constant percentage rate every period. Unlike a flat perpetuity — which pays the same amount forever — a growing perpetuity grows at a steady rate g, making it far more realistic for modeling real-world income streams such as corporate dividends, rental income, or royalty payments that tend to increase alongside inflation or business growth.

The concept is central to corporate finance, equity valuation, and long-run investment analysis. When analysts want to estimate the terminal value of a business or project beyond a forecast horizon, they commonly apply the growing perpetuity formula to the final projected cash flow. Understanding this model allows investors to quickly convert an infinite series of growing cash flows into a single, comparable present-value figure.

The growing perpetuity calculator on this page computes the present value using the Gordon Growth Model (also called the dividend discount model in equity contexts). You enter the first expected payment, the constant annual growth rate, and your required rate of return. The tool instantly calculates the present value, along with projected payments in year 5 and year 10, the effective net yield, and — when growth is positive — the number of years it takes for a payment to double.

This model has one critical mathematical constraint: the growth rate g must be strictly less than the discount rate r. When g equals or exceeds r, the denominator becomes zero or negative, which would imply an infinite or nonsensical present value. In practice this constraint is almost always met for mature, stable assets, but care is needed when using the model for high-growth early-stage companies where near-term growth may temporarily outpace the discount rate.

The present value of a growing perpetuity is derived from discounting an infinite geometric series of cash flows. The closed-form result — valid when r > g — reduces to a remarkably simple expression known as the Gordon Growth Model:

Every variable in the formula has a precise financial meaning. D1 (or PMT) is the next payment — the one expected at the end of the first period, not the most recent payment already paid. This is a common source of error: if a stock just paid a dividend D0, you must first grow it by one period to get D1 = D0 × (1 + g) before plugging into the formula. The discount rate r is the investor's required rate of return, reflecting the opportunity cost of capital and the risk of the cash flows. The growth rate g is the assumed constant annual percentage increase in the payment stream.

The denominator (r − g) is sometimes called the capitalization rate or net yield. A smaller denominator means a higher present value, which explains why small changes in either r or g can have dramatic effects on valuation — a sensitivity that practitioners must account for carefully.

Using this growing perpetuity calculator is straightforward. Enter three inputs and the results update instantly.

• First Payment (D1): The cash flow you expect to receive at the end of the very first period. This must be a positive number. For dividend discount model applications, this is the dividend per share expected next year, not the dividend just paid.
• Growth Rate (g %): The constant annual percentage rate at which every future payment will grow. For a company with steady 3% annual dividend growth, enter 3. For inflation-linked rental income in a 2% inflation environment, enter 2.
• Discount Rate (r %): Your required rate of return, reflecting risk and opportunity cost. This is often estimated using the Capital Asset Pricing Model (CAPM) for equities, or approximated by comparable bond yields plus an equity risk premium.

The calculator immediately outputs:

• Present Value: The lump-sum equivalent of the entire infinite growing payment stream today.
• Year 5 and Year 10 Projected Payments: Computed as D1 × (1 + g)ⁿ, showing how the payment stream grows over time.
• Effective Yield (r − g): The capitalization rate as a percentage — a useful shorthand for how much you are implicitly earning net of growth.
• Years to Double Payment: Derived from the doubling-time formula ln(2) / ln(1 + g), showing how long until payments are twice as large as D1.

If you enter a growth rate equal to or greater than the discount rate, the calculator will display an error. This is by design — the formula is only mathematically valid when g < r.

The growing perpetuity model has broad applications across finance and investment. Below are the most common contexts where practitioners rely on this formula.

Dividend Discount Model (DDM) for Stock Valuation

The most famous application is the Dividend Discount Model for valuing dividend-paying stocks. A stock's intrinsic value equals the present value of all future dividends. For a mature company with stable, growing dividends, the Gordon Growth Model gives a one-step valuation: intrinsic value = D1 / (r − g). If a stock is trading significantly below this value, it may be undervalued; if it trades above, it may be overpriced relative to its fundamentals.

Real Estate and Rental Income

Investors use the growing perpetuity framework to value commercial properties or rental portfolios. Annual rent escalations of 2–3% per year, combined with a required cap rate, yield a property value estimate. This is essentially the same math as the DDM but applied to net operating income (NOI) rather than dividends.

Terminal Value in DCF Analysis

When building a discounted cash flow (DCF) model, analysts project free cash flows for 5–10 years and then estimate a terminal value representing all subsequent cash flows. The most common method applies the Gordon Growth Model to the final projected year's cash flow, assuming it grows at a stable rate (often GDP growth or inflation) forever. This terminal value can represent 60–80% of the total DCF value, so the choice of g and r matters enormously.

Perpetual Bonds and Preferred Stock

Some financial instruments like consols (perpetual bonds) or preferred stock with growing dividends are directly valued using this formula. Understanding the present value mechanics helps investors assess whether the current market price fairly reflects expected payment growth and required return.

Business Valuation and M&A

In mergers and acquisitions, terminal value estimation using the growing perpetuity formula is standard practice. Investment bankers and business appraisers use it to assign a steady-state value to a going concern once it reaches a stable growth phase.

The growing perpetuity formula is elegant but highly sensitive to its inputs. Small changes in either the discount rate r or growth rate g can produce dramatically different valuations. This sensitivity is a feature of the model's mathematics: because (r − g) appears in the denominator, any narrowing of the spread between r and g causes the present value to rise sharply. For example, reducing r from 10% to 9% while holding g at 3% changes the denominator from 0.07 to 0.06 — a 14% reduction that increases the valuation by approximately 17%.

This extreme sensitivity means analysts should always run scenario analyses when using growing perpetuity valuations. Consider at minimum a base case, a bear case (lower g or higher r), and a bull case (higher g or lower r). The spread of outcomes reveals how much uncertainty is embedded in any single-point estimate.

Key Limitations to Keep in Mind

• Constant growth assumption: The model requires a single, constant growth rate forever. Real businesses, properties, and cash flows do not grow at precisely constant rates. For companies in high-growth or cyclical phases, the model can seriously overstate or understate value.
• Growth rate must be less than discount rate: This mathematical constraint limits applicability to mature, stable assets. For startups or high-growth firms, a multi-stage model is more appropriate.
• Discount rate subjectivity: Estimating r requires judgment about risk, opportunity cost, and market conditions — all of which can vary significantly across analysts.
• Inflation and real vs. nominal rates: Both g and r should be expressed in consistent terms — either both nominal or both real. Mixing real growth with a nominal discount rate is a common error that inflates valuations.
• No consideration of capital structure changes: The basic model assumes the payment structure remains proportional to value indefinitely, which may not hold in leveraged buyouts or restructurings.

Despite these limitations, the growing perpetuity calculator remains one of the most widely used tools in finance because of its simplicity, transparency, and direct link to fundamental value drivers.