Why Can’t We Calculate the Required Return (Ke) from the Gordon-Shapiro Model?
In finance, the Gordon-Shapiro model, also known as the Dividend Discount Model (DDM), is a popular valuation tool used to estimate the intrinsic value of a company’s stock based on the present value of its future dividends. The model assumes that dividends grow at a constant rate and that the discount rate, or required return (Ke), is greater than the growth rate. The formula for the Gordon-Shapiro model is:
P0 = Div0 (1+g) / (Ke – g)
Where:
- P0 is the current stock price
- Div0 is the current dividend
- g is the constant growth rate of dividends
- Ke is the required return or cost of equity
While the Gordon-Shapiro model is a valuable tool for valuation, it’s important to understand its limitations and why it’s not always suitable for calculating the required return (Ke). Here’s a breakdown of the reasons why we can’t rely solely on the Gordon-Shapiro model for Ke calculation:
Assumptions and Limitations of the Gordon-Shapiro Model
The Gordon-Shapiro model relies on several key assumptions that may not always hold true in real-world scenarios. These assumptions limit its applicability for calculating Ke:
- **Constant Dividend Growth:** The model assumes that dividends grow at a constant rate forever. In reality, dividend growth is often unpredictable and can fluctuate significantly over time. Companies may adjust their dividend policies based on factors like profitability, investment opportunities, and market conditions.
- **Stable Discount Rate:** The model assumes a constant discount rate (Ke) over time. However, the required return can change due to factors like risk aversion, inflation, and market interest rates. These changes can impact the accuracy of the model’s results.
- **No Growth in Terminal Value:** The model assumes that the company’s value converges to zero in the long run. This assumption may not be realistic for companies with sustainable growth prospects or those operating in industries with long-term growth potential.
- **No Consideration for Risk:** The model doesn’t explicitly account for the risk associated with the company’s future cash flows. This can lead to an inaccurate estimate of Ke, especially for companies with high levels of risk.
Why CAPM is Preferred for Calculating Ke
The Capital Asset Pricing Model (CAPM) is a widely accepted model for calculating the required return (Ke) for a company’s stock. It explicitly considers the risk associated with the investment and provides a more comprehensive approach to determining the appropriate discount rate. Here’s why CAPM is preferred over the Gordon-Shapiro model for calculating Ke:
- **Risk-Adjusted Return:** CAPM incorporates the concept of beta, which measures the volatility of a stock relative to the overall market. This allows for a risk-adjusted return calculation, reflecting the specific risk profile of the company.
- **Market-Based Approach:** CAPM uses market data, such as the risk-free rate and the market risk premium, to determine the required return. This provides a more objective and market-driven approach compared to the Gordon-Shapiro model’s reliance on dividend growth assumptions.
- **Flexibility and Adaptability:** CAPM is more flexible and adaptable to changing market conditions. It can be easily adjusted to reflect changes in risk aversion, inflation, and market interest rates, providing a more dynamic and accurate estimate of Ke.
Example: Comparing Gordon-Shapiro and CAPM
Let’s consider a hypothetical example to illustrate the differences between the two models. Suppose a company has a current dividend of $2 per share, a dividend growth rate of 5%, and a current stock price of $50. Using the Gordon-Shapiro model, we can calculate the required return (Ke) as follows:
Ke = Div0 (1+g) / P0 + g
Ke = $2 (1+0.05) / $50 + 0.05
Ke = 0.09 or 9%
Now, let’s assume that the company’s beta is 1.2, the risk-free rate is 2%, and the market risk premium is 5%. Using CAPM, we can calculate the required return (Ke) as follows:
Ke = Risk-free rate + Beta * Market risk premium
Ke = 2% + 1.2 * 5%
Ke = 8%
As you can see, the Gordon-Shapiro model estimates a required return of 9%, while CAPM estimates a required return of 8%. This difference highlights the potential discrepancies between the two models, particularly when assumptions about dividend growth and risk are not met.
Conclusion
While the Gordon-Shapiro model can be a useful tool for valuation, it’s not suitable for calculating the required return (Ke) due to its limitations and assumptions. CAPM provides a more comprehensive and risk-adjusted approach to determining the appropriate discount rate for a company’s stock. By incorporating market data and considering the specific risk profile of the company, CAPM offers a more reliable and accurate estimate of Ke, making it the preferred model for investment decisions.