Investment specialist and expert in advanced equity and dividend valuation models.
The **Present Value of Perpetuity with Growth Calculator** determines the current worth of an asset that promises a stream of cash flows expected to grow at a constant rate forever. This is the foundation of the Gordon Growth Model. Enter any three of the core parameters to solve for the missing one.
Present Value of Perpetuity with Growth Calculator
Instructions: Enter values for any three of the four core parameters to solve for the missing one.
Growth Perpetuity Metrics
Growing Perpetuity Present Value Formula
The Present Value is calculated using a modified perpetuity model (Gordon Growth Model):
$$PV = \frac{C_1}{R – g}$$ Formula Source: InvestopediaVariables Explained (Q, F, P, V – Parameters)
- $C_1$ (Cash Flow, $Q$): The expected cash flow in the next period (e.g., next year’s dividend).
- $R$ (Discount Rate, $F$): The required rate of return (expressed as a decimal).
- $g$ (Growth Rate, $P$): The perpetual annual growth rate of the cash flows (expressed as a decimal).
- $PV$ (Present Value, $V$): The current worth of the growing stream of cash flows.
Related Valuation and Investment Calculators
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- Present Value of Perpetuity Calculator (Zero Growth)
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What is a Growing Perpetuity?
A **growing perpetuity** is a stream of cash flows that is expected to continue indefinitely, with each successive cash flow growing at a constant, fixed rate ($g$). This model, particularly known as the Gordon Growth Model (GGM) when applied to stocks, assumes a stable, mature company with predictable growth.
The key assumption for this model to work is that the required rate of return ($R$) must be strictly greater than the perpetual growth rate ($g$). If $R \le g$, the denominator becomes zero or negative, making the present value infinite or nonsensical. This constraint ensures the model remains mathematically sound.
How to Calculate Growing Perpetuity PV (Example)
Assume a company will pay a dividend of \$3.00 next year ($C_1$). The required return ($R$) is 10% (0.10), and the dividend is expected to grow by 5% (0.05) forever.
- Step 1: Determine the Denominator ($R – g$)
$$R – g = 0.10 – 0.05 = \mathbf{0.05}$$
- Step 2: Apply the Formula
$$PV = \frac{C_1}{R – g}$$
- Step 3: Calculate the Intrinsic Value
$$PV = \frac{\$3.00}{0.05} = \mathbf{\$60.00}$$
The Present Value of this Growing Perpetuity is $\mathbf{\$60.00}$.
Frequently Asked Questions (FAQ)
It is most useful for valuing companies (especially stable, dividend-paying ones) where the growth rate is highly predictable and sustainable over the long term. It forms the basis for calculating a company’s terminal value in DCF models.
The required rate of return ($R$) must be greater than the growth rate ($g$) to ensure the present value of the infinite cash flows remains finite. If $R$ were less than $g$, it would imply that the cash flows are growing faster than the rate at which they are discounted, resulting in an infinite present value, which is illogical.
Yes, the Gordon Growth Model (GGM) is a specific application of the DDM for the perpetual growth phase. GGM is often used to calculate the terminal value, which is then discounted back to the present value in multi-stage DDM models.
$C_0$ is the cash flow (e.g., dividend) that *just* occurred (current period). $C_1$ is the cash flow expected *next* period. The GGM formula requires $C_1$, which is calculated as $C_0 \times (1 + g)$.