This Gordon Growth Model (GGM) Calculator accurately determines the theoretical intrinsic value of a stock, or solves for the dividend, required return, or growth rate, based on the perpetual growth dividend discount model.
Welcome to the **Gordon Growth Model Calculator**. The GGM is a variation of the Dividend Discount Model (DDM) used to determine the intrinsic value of a stock, assuming that dividends will grow at a constant rate perpetually. This tool uses the core relationship to solve for the stock’s Price ($P$), the next expected Dividend ($D1$), the Required Rate of Return ($r$), or the Perpetual Growth Rate ($g$).
Gordon Growth Model Calculator
GGM Formulas
The core relationship is: $P = \frac{D1}{r – g}$. Note that $r$ and $g$ must be decimals for calculation.
1. Solve for Price (P):
$$ P = \frac{D1}{r – g} $$
2. Solve for Next Dividend ($D1$):
$$ D1 = P \times (r – g) $$
3. Solve for Required Return ($r$):
$$ r = g + \frac{D1}{P} $$
4. Solve for Growth Rate ($g$):
$$ g = r – \frac{D1}{P} $$
Formula Source: Investopedia – Gordon Growth Model
Variables Explained
- P – Share Price: The computed intrinsic value or current market price of the stock. (Currency)
- D1 – Expected Dividend Next Year: The dividend expected to be paid in the upcoming year ($D0 \times (1 + g)$). (Currency)
- r – Required Rate of Return: The minimum return expected by the investor (Cost of Equity). (Percent)
- g – Perpetual Growth Rate: The constant, sustainable rate at which dividends are expected to grow. (Percent)
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What is the Gordon Growth Model?
The Gordon Growth Model (GGM), or perpetuity with growth model, is a quantitative model used to value a stock. It assumes the current price of the stock is the present value of all its future dividend payments, discounted back at the required rate of return. Unlike general discounted cash flow (DCF) models, the GGM provides a streamlined way to calculate terminal value based on the assumption of a stable, constant rate of dividend growth into perpetuity.
The primary strength of the GGM is its simplicity and its ability to incorporate expected future growth directly into the valuation. However, its accuracy relies entirely on two critical assumptions: first, that the company pays dividends; and second, that dividends will grow at a perfectly constant rate forever, which is often unrealistic in the real world.
The GGM is most appropriate for valuing mature, stable companies with a long history of paying and increasing dividends, such as utility companies or well-established consumer staples businesses.
How to Calculate Required Rate of Return (Example)
A stock is trading at a **Share Price** ($P$) of **$40.00**. The **Expected Dividend Next Year** ($D1$) is **$2.50**. The **Perpetual Growth Rate** ($g$) is estimated to be **3.0%**. What is the missing **Required Rate of Return** ($r$)?
- Determine the Missing Variable: Required Rate of Return ($r$) is missing.
- Convert Rates to Decimal: $g = 3.0\% \div 100 = 0.03$.
- Apply Formula: $$ r = g + \frac{D1}{P} $$
- Substitute Values: $r = 0.03 + \frac{\$2.50}{\$40.00}$.
- Calculate Dividend Yield: $\frac{\$2.50}{\$40.00} = 0.0625$.
- Calculate R: $r = 0.03 + 0.0625 = 0.0925$.
- Result: The Required Rate of Return ($r$) is **9.25%**. (Check: $r=9.25\% > g=3.0\%$. Valid.)
Frequently Asked Questions (FAQ)
The biggest limitation is the assumption that the growth rate ($g$) is constant and perpetual. In reality, no company can maintain the same growth rate forever. Also, the model breaks down completely if the required return ($r$) is equal to or less than the growth rate ($g$).
Why must the required return ($r$) be greater than the growth rate ($g$)?The GGM relies on discounting a stream of perpetual cash flows. If $r \le g$, the denominator $(r – g)$ would be zero or negative, resulting in a calculated price ($P$) that is infinite or negative, which is mathematically impossible for a stock price. This is known as the “no-growth” condition failure.
What inputs should I use for $r$ and $g$?$r$ (Required Return) is often determined using the CAPM (Capital Asset Pricing Model) or WACC (Weighted Average Cost of Capital). $g$ (Perpetual Growth) is typically estimated using the risk-free rate, the inflation rate, or the long-term GDP growth rate of the country where the company operates.
Is the GGM used for young growth companies?Generally, no. Young growth companies typically do not pay dividends and have extremely high, volatile growth rates that cannot be modeled as perpetual and constant. Multi-stage DDM models are usually more appropriate for such firms.