What Is the Present Value of a Growing Perpetuity?

A growing perpetuity is an infinite stream of cash flows that increases at a steady rate every year. Imagine owning an investment that pays you $1,000 this year, $1,050 next year, $1,102.50 the year after, and so on—forever. This concept is used to value assets like dividend-growing stocks, rental properties with rising rents, or royalties tied to inflation. The present value tells you what that ever-growing income is worth today.

For example, a company that raises its dividend by 3% annually can be modeled as a growing perpetuity. Investors use this to decide if the stock is fairly priced relative to its growth potential.

How to Calculate the Present Value of a Growing Perpetuity

The formula is:
PV = Cash Flow / (Discount Rate − Growth Rate)

First, determine the initial cash flow (e.g., $10,000 in Year 1). Next, estimate the annual growth rate (e.g., 2% for inflation-adjusted income). Finally, subtract the growth rate from the discount rate (your required return) and divide the cash flow by this result.

For example, a rental property generates $20,000 annually, growing at 3% per year. With a 7% discount rate:

PV = $20,000 / (0.07 − 0.03) = $500,000

This means the property is worth $500,000 today, accounting for both its current income and future growth.

Why Use the Growing Perpetuity Formula?

This formula adjusts for rising cash flows, making it more realistic than a flat perpetuity. It’s ideal for valuing stocks with growing dividends, real estate in appreciating markets, or businesses with expanding revenues. Investors use it to avoid undervaluing assets that generate increasing income over time.

For instance, a dividend stock paying $5/share today, growing at 4% annually, with a 10% required return, has a PV of $83.33/share ($5 / (0.10 − 0.04)). If the stock trades below this, it might be undervalued—a signal to buy.

Interpreting the Results

The growth rate must be lower than the discount rate—otherwise, the formula breaks down (you can’t divide by zero or a negative number). A 5% growth rate with a 5% discount rate suggests infinite value, which is unrealistic. Always ensure the discount rate exceeds the growth rate.

A higher growth rate boosts the present value. For example, a $10,000 cash flow at a 5% discount rate is worth:
- $200,000 with 0% growth ($10,000 / 0.05).
- $333,333 with 2% growth ($10,000 / (0.05 − 0.02)).
This shows how growth transforms long-term value.

Practical Applications of the Formula

Companies use this to value projects with recurring, growing income. A solar farm generating $50,000 yearly, increasing by 3% annually, with a 9% discount rate, is worth $833,333 today. This helps decide whether to fund the project.

Retirees use it to plan inflation-adjusted withdrawals. If you need $60,000 annually, growing at 2% to keep up with inflation, and expect a 6% return, you’d need $1,500,000 upfront ($60,000 / (0.06 − 0.02)). This ensures your income retains purchasing power.

Common Mistakes to Avoid

Overestimating the growth rate is a classic error. A company might project 8% annual dividend growth, but if the industry average is 3%, the calculation becomes overly optimistic. Always use conservative, sustainable growth estimates.

Ignoring risk is another pitfall. A high-growth startup might use a 12% discount rate to account for uncertainty, while a utility company with stable cash flows uses 5%. Mismatching rates and growth leads to inaccurate valuations.

Real-World Example: Valuing a Dividend Stock

Let’s analyze Company X, which pays a $4 annual dividend, growing at 5% yearly. Investors require an 11% return due to market volatility.
Using the formula:

PV = $4 / (0.11 − 0.05) = $66.67

If the stock trades at $60, it’s undervalued—a potential buy. If it’s at $80, it’s overpriced. This helps investors make data-driven decisions.

Adjusting for Real-World Complexity

In reality, growth rates aren’t constant forever. A company might grow dividends at 6% for a decade, then slow to 3%. For such cases, use a two-stage model: calculate the PV of the high-growth phase, then add the PV of the stabilized perpetuity. This hybrid approach offers more precision.

For example, a tech firm grows cash flows at 8% for 5 years, then 3% indefinitely. Discount each high-growth year separately, then apply the perpetuity formula to the stabilized phase. Sum both values for the total PV.

Conclusion

The present value of a growing perpetuity formula (PV = Cash Flow / (Discount Rate − Growth Rate)) is a cornerstone of finance for valuing assets with rising cash flows. From dividend stocks to rental properties, it bridges today’s investment with tomorrow’s growth.

By mastering this tool, investors and businesses can make smarter decisions, balancing risk, growth, and time. Just remember: realistic growth rates and careful discount rate selection are key. Use it wisely, and you’ll unlock the power to see forever—in today’s dollars.