DDM – Dividend Discount Model Calculator
Use this tool to estimate the intrinsic value of a stock using the Gordon Growth Model, a simplified version of the Dividend Discount Model (DDM).
This model assumes that dividends grow at a constant rate indefinitely. Ensure your inputs are consistent (e.g., 'r' and 'g' as decimals).
Enter Stock Data
Understanding the Dividend Discount Model (DDM) - Gordon Growth Model
What is the Gordon Growth Model?
The Gordon Growth Model is a specific, simplified version of the Dividend Discount Model (DDM). It is used to determine the intrinsic value of a stock based on a future series of dividends that are assumed to grow at a constant rate. It is calculated as the present value of an infinite series of future dividends.
The Formula
The formula for the Gordon Growth Model is:
P = D1 / (r - g)
- P = Current Stock Price (Intrinsic Value)
- D1 = Expected Dividend Per Share One Year From Now
- r = Required Rate of Return (as a decimal)
- g = Expected Dividend Growth Rate (as a decimal)
This model is most suitable for mature companies with a stable history of dividend payments and a predictable, constant growth rate.
Important Assumptions and Limitations
- Dividends grow at a constant rate (g) forever.
- The required rate of return (r) is constant forever.
- The required rate of return (r) must be strictly greater than the dividend growth rate (g). If r ≤ g, the denominator becomes zero or negative, leading to an infinite or negative value, which is nonsensical in this context.
- It does not work for companies that do not pay dividends.
- Finding accurate values for D1, r, and especially g can be challenging and subjective.
DDM Calculation Examples
Click on an example to see the details:
Example 1: Standard Growth
Scenario: A company is expected to pay a dividend of $2.00 next year. Your required rate of return is 10%, and you expect the dividend to grow at 5% annually.
1. Known Values: D1 = $2.00, r = 10% (0.10), g = 5% (0.05).
2. Formula: P = D1 / (r - g)
3. Calculation: P = 2.00 / (0.10 - 0.05) = 2.00 / 0.05
4. Result: P = $40.00
Conclusion: The estimated intrinsic value is $40.00 per share.
Example 2: Higher Required Return
Scenario: Using the same company as Ex 1, but you require a higher return of 12% due to increased risk.
1. Known Values: D1 = $2.00, r = 12% (0.12), g = 5% (0.05).
2. Formula: P = D1 / (r - g)
3. Calculation: P = 2.00 / (0.12 - 0.05) = 2.00 / 0.07
4. Result: P ≈ $28.57
Conclusion: A higher required return lowers the intrinsic value.
Example 3: Lower Growth Rate
Scenario: Using the company from Ex 1, but you only expect a dividend growth rate of 3%.
1. Known Values: D1 = $2.00, r = 10% (0.10), g = 3% (0.03).
2. Formula: P = D1 / (r - g)
3. Calculation: P = 2.00 / (0.10 - 0.03) = 2.00 / 0.07
4. Result: P ≈ $28.57
Conclusion: A lower growth rate also lowers the intrinsic value.
Example 4: Zero Growth
Scenario: A very mature company is expected to pay a $3.00 dividend next year with zero growth (g=0). Your required return is 8%.
1. Known Values: D1 = $3.00, r = 8% (0.08), g = 0% (0.00).
2. Formula: P = D1 / (r - g)
3. Calculation: P = 3.00 / (0.08 - 0.00) = 3.00 / 0.08
4. Result: P = $37.50
Conclusion: The value is the perpetual stream of $3 dividends discounted at 8%.
Example 5: High Growth (but still < r)
Scenario: A promising company has D1 = $1.00, your required return is 15%, and you expect 10% dividend growth.
1. Known Values: D1 = $1.00, r = 15% (0.15), g = 10% (0.10).
2. Formula: P = D1 / (r - g)
3. Calculation: P = 1.00 / (0.15 - 0.10) = 1.00 / 0.05
4. Result: P = $20.00
Conclusion: High growth can lead to a higher value relative to the dividend amount.
Example 6: Calculating D1 from D0
Scenario: A company just paid a dividend (D0) of $1.80. You expect 6% growth (g=0.06) and require a 11% return (r=0.11). First calculate D1.
1. Calculate D1: D1 = D0 * (1 + g) = 1.80 * (1 + 0.06) = 1.80 * 1.06 = $1.908
2. Known Values for DDM: D1 = $1.908, r = 11% (0.11), g = 6% (0.06).
3. Formula: P = D1 / (r - g)
4. Calculation: P = 1.908 / (0.11 - 0.06) = 1.908 / 0.05
5. Result: P = $38.16
Conclusion: If you know D0 and g, calculate D1 before using the model.
Example 7: Sensitivity - Impact of R
Scenario: A stock has D1 = $1.50 and g = 4%. Calculate the value if r = 9% vs r = 10%.
Case A (r=9%): P = 1.50 / (0.09 - 0.04) = 1.50 / 0.05 = $30.00
Case B (r=10%): P = 1.50 / (0.10 - 0.04) = 1.50 / 0.06 = $25.00
Conclusion: A small change in the required return can significantly impact the calculated value.
Example 8: Sensitivity - Impact of G
Scenario: A stock has D1 = $1.50 and r = 10%. Calculate the value if g = 4% vs g = 5%.
Case A (g=4%): P = 1.50 / (0.10 - 0.04) = 1.50 / 0.06 = $25.00
Case B (g=5%): P = 1.50 / (0.10 - 0.05) = 1.50 / 0.05 = $30.00
Conclusion: A small change in the growth rate assumption can significantly impact the calculated value.
Example 9: D1 is known, inputs as percentages
Scenario: You find data suggesting D1 = $0.85, r = 13%, and g = 7%. (This calculator expects decimals, but showing calculation from percentages).
1. Convert to decimals: D1 = $0.85, r = 0.13, g = 0.07.
2. Formula: P = D1 / (r - g)
3. Calculation: P = 0.85 / (0.13 - 0.07) = 0.85 / 0.06
4. Result: P ≈ $14.17
Conclusion: Always ensure 'r' and 'g' are used as decimals in the formula.
Example 10: Low Dividend, Moderate Growth
Scenario: A company pays a relatively small dividend (D1 = $0.50) but is expected to grow dividends at a moderate rate of 6%. Your required return is 11%.
1. Known Values: D1 = $0.50, r = 11% (0.11), g = 6% (0.06).
2. Formula: P = D1 / (r - g)
3. Calculation: P = 0.50 / (0.11 - 0.06) = 0.50 / 0.05
4. Result: P = $10.00
Conclusion: Even a low current dividend can justify a higher stock value if growth is strong and the required return is relatively low.
Frequently Asked Questions about DDM & Gordon Growth Model
1. What is the main purpose of the Dividend Discount Model (DDM)?
The main purpose is to estimate the intrinsic value of a stock based on the present value of its expected future dividends.
2. What's the difference between DDM and the Gordon Growth Model?
The Gordon Growth Model is a specific type of DDM that assumes dividends grow at a constant rate indefinitely. Other DDM models allow for variable growth rates over time.
3. What do D1, r, and g represent in the formula?
D1 is the expected dividend per share *one year from now*. 'r' is your required rate of return for the investment. 'g' is the expected constant annual growth rate of the dividends.
4. Why must the required rate of return (r) be greater than the growth rate (g)?
If r is less than or equal to g, the denominator (r - g) becomes zero or negative. This results in an infinite or negative stock value, which is not logically possible in this valuation model. It reflects the assumption that the present value of future dividends must converge to a finite number.
5. How do I estimate the inputs (D1, r, g)?
Estimating inputs is subjective. D1 can often be estimated based on the last dividend paid (D0) and an expected short-term growth rate (D1 = D0 * (1+g)). The required rate of return (r) often relates to your personal investment goals or can be estimated using models like the Capital Asset Pricing Model (CAPM). The growth rate (g) is the most difficult; analysts often use historical growth, industry averages, or management guidance, but it's a critical assumption.
6. Can I use this calculator for any stock?
No. The Gordon Growth Model is best suited for mature, stable companies with a history of paying dividends that are expected to grow at a relatively constant rate. It is not appropriate for growth stocks that pay no dividends or have highly variable growth, or for companies in distress.
7. How accurate is the DDM?
The accuracy of the DDM depends heavily on the accuracy of its inputs, particularly the growth rate (g). Small changes in 'r' or 'g' can significantly impact the calculated value, making it sensitive to assumptions. It's a theoretical model providing an estimate, not a precise market price prediction.
8. What does the calculated stock value mean?
The calculated value is an estimate of the stock's intrinsic value based on the model's assumptions. If the current market price is significantly below this value, the stock might be considered undervalued according to this model, and vice versa.
9. What happens if I input r and g as percentages (e.g., 10 instead of 0.10)?
The calculator expects 'r' and 'g' as decimals (e.g., 0.10 for 10%). Inputting them as whole percentages will result in an incorrect, likely very small, calculated value because the denominator (r-g) will be calculated using the percentage numbers directly, not their decimal equivalents.
10. Are there other types of Dividend Discount Models?
Yes, the Gordon Growth Model is the simplest. There are also multi-stage DDM models that allow for different growth rates over different periods (e.g., a high growth phase, followed by a transition phase, and finally a constant growth phase) before reaching a terminal value calculation.
