Calculate Cost of Common Equity Using Gordon Model

Interactive Gordon Growth Model Calculator

Gordon Growth Model Inputs and Intermediate Values

Metric	Value	Unit
Expected Dividend Next Year (D1)	–.–	Currency
Current Stock Price (P0)	–.–	Currency
Constant Growth Rate (g)	–.–	Percent (%)
Implied Cost of Equity (Ke)	–.–	Percent (%)

What is the Cost of Common Equity Using the Gordon Model?

The cost of common equity, often calculated using the Gordon Growth Model (also known as the Dividend Discount Model or DDM), represents the rate of return a company expects to pay its equity investors to compensate them for the risk of owning its stock. In simpler terms, it’s the minimum return shareholders require from an investment in a company’s stock. The Gordon Growth Model is a widely used valuation method that estimates this cost by considering the expected future dividends and their growth rate, relative to the current stock price. This metric is crucial for financial managers when making investment decisions, evaluating project profitability, and determining the company’s overall cost of capital (WACC).

Who Should Use It?

The Gordon Growth Model is most applicable to mature, stable companies that have a consistent history of paying dividends and are expected to grow those dividends at a relatively constant rate indefinitely. Investors and financial analysts use it to:

• Estimate the intrinsic value of a stock.
• Determine the required rate of return for equity investors.
• Compare the cost of equity to the expected returns from potential projects.
• Assess the risk associated with investing in a particular company.

Common Misconceptions

Several misconceptions surround the Gordon Growth Model:

• It applies to all companies: The model is less suitable for high-growth companies that reinvest earnings rather than pay dividends, or companies with erratic dividend patterns.
• Growth is always constant: In reality, growth rates fluctuate. The model assumes a perpetual constant growth rate, which is a simplification.
• It’s the only way to determine equity cost: While popular, other models like the Capital Asset Pricing Model (CAPM) are also widely used and may be more appropriate in certain scenarios.

Cost of Common Equity Formula and Mathematical Explanation

The Gordon Growth Model provides a straightforward way to calculate the cost of common equity (Ke). The core idea is that the current stock price (P0) should reflect the present value of all expected future dividends. Assuming dividends grow at a constant rate (g) indefinitely, the formula is derived as follows:

Step-by-Step Derivation:

1. The price of a stock (P0) is the present value of all future dividends.
2. If the dividend in the next period is D1, and it grows at a constant rate ‘g’ per period, the future dividends are: D1, D1(1+g), D1(1+g)², and so on.
3. The present value of these future dividends, discounted at the required rate of return (Ke), forms a geometric series:
   P0 = D1 / (1+Ke)¹ + D1(1+g) / (1+Ke)² + D1(1+g)² / (1+Ke)³ + …
4. For this infinite series to converge (meaning the present value is finite and the model works), the discount rate (Ke) must be greater than the growth rate (g).
5. By rearranging and simplifying this infinite geometric series, we arrive at the Gordon Growth Model formula:
   P0 = D1 / (Ke – g)
6. To find the cost of equity (Ke), we rearrange the formula:
   P0 * (Ke – g) = D1
   Ke – g = D1 / P0
   Ke = (D1 / P0) + g

Variable Explanations:

• Ke (Cost of Equity): The required rate of return for equity investors. This is what we aim to calculate. It represents the implicit cost to the company of raising equity capital.
• D1 (Expected Dividend Next Year): The dividend per share expected to be paid out over the next 12 months. It’s crucial to use the *next* year’s dividend, not the current one.
• P0 (Current Stock Price): The current market price of one share of the company’s stock. This reflects the market’s current valuation of the company’s future earnings and dividends.
• g (Constant Growth Rate): The expected constant annual rate at which dividends are projected to grow indefinitely. This rate should be less than the cost of equity (g < Ke).

Variables Table:

Gordon Growth Model Variables

Variable	Meaning	Unit	Typical Range
Ke	Cost of Common Equity	Percent (%)	8% – 15% (Can vary widely)
D1	Expected Dividend Per Share Next Year	Currency (e.g., $)	Varies by company
P0	Current Market Price Per Share	Currency (e.g., $)	Varies by company
g	Constant Dividend Growth Rate	Percent (%)	Typically 2% – 6% (Must be less than Ke)

Practical Examples (Real-World Use Cases)

Example 1: Stable Utility Company

A well-established utility company, “StablePower Inc.,” is known for its consistent dividend payments and predictable growth. Analysts expect StablePower Inc. to pay a dividend of $3.00 per share next year (D1). The current stock price (P0) is trading at $40.00 per share. Historical analysis suggests a stable dividend growth rate of 4.00% per year (g).

Inputs:

• D1 = $3.00
• P0 = $40.00
• g = 4.00%

Calculation using the Gordon Model:

Ke = (D1 / P0) + g

Ke = ($3.00 / $40.00) + 0.04

Ke = 0.075 + 0.04

Ke = 0.115

Result: The cost of common equity for StablePower Inc. is 11.50%.

Financial Interpretation: Shareholders of StablePower Inc. require an annual return of at least 11.50% to compensate them for the risk associated with owning the stock. If the company’s projects are expected to yield returns less than this, it may not be advisable to pursue them using equity financing.

Example 2: Established Consumer Goods Company

Consider “Global Brands Corp.,” a large consumer goods company. The company is forecasted to pay $2.20 per share in dividends next year (D1). Its current stock price (P0) is $55.00. Management projects a sustainable dividend growth rate (g) of 5.00% annually.

Inputs:

• D1 = $2.20
• P0 = $55.00
• g = 5.00%

Calculation using the Gordon Model:

Ke = (D1 / P0) + g

Ke = ($2.20 / $55.00) + 0.05

Ke = 0.04 + 0.05

Ke = 0.09

Result: The cost of common equity for Global Brands Corp. is 9.00%.

Financial Interpretation: This result indicates that Global Brands Corp. needs to generate returns of at least 9.00% on its equity-financed investments to satisfy its shareholders. This relatively lower cost of equity compared to some growth companies might be due to its stability and lower perceived risk.

How to Use This Cost of Common Equity Calculator

Our calculator simplifies the process of applying the Gordon Growth Model. Follow these steps for accurate results:

Step-by-Step Instructions:

1. Input Expected Dividend Next Year (D1): Enter the total amount of dividend you expect the company to pay per share over the next 12 months.
2. Input Current Stock Price (P0): Enter the current market price of a single share of the stock.
3. Input Constant Growth Rate (g): Enter the expected constant annual percentage growth rate of dividends. Ensure this rate is reasonable and sustainable for the company in the long term. Remember to enter it as a percentage (e.g., 5 for 5%).
4. Click ‘Calculate Cost of Equity’: The calculator will process your inputs.
5. Review Results: The primary result, the Cost of Equity (Ke), will be displayed prominently. Intermediate values like D1, P0, g, and the calculated implied Ke are also shown for clarity.
6. Use ‘Reset Defaults’: If you want to start over or revert to sample values, click this button.
7. Use ‘Copy Results’: This button allows you to easily copy the calculated main result, intermediate values, and key assumptions to your clipboard for use in reports or other documents.

How to Read Results

The main output is the **Cost of Equity (Ke)**, expressed as a percentage. This figure represents the minimum annual return required by shareholders. The intermediate values confirm the inputs used and the calculated implied cost of equity, providing transparency.

Decision-Making Guidance

The calculated cost of equity is a critical benchmark. Companies should compare the expected returns on potential projects and investments against their cost of equity. If a project’s expected return exceeds Ke, it is generally considered value-creating. Conversely, projects earning less than Ke may destroy shareholder value.

Key Factors That Affect Cost of Common Equity Results

Several factors significantly influence the outcome of the Gordon Growth Model calculation and, consequently, the perceived cost of common equity:

1. Dividend Growth Rate (g): A higher expected growth rate directly increases the cost of equity. If investors anticipate faster dividend increases, they will demand a higher overall return. However, an unrealistically high ‘g’ can lead to nonsensical results, highlighting the model’s sensitivity to this assumption.
2. Current Stock Price (P0): A lower stock price, holding other factors constant, results in a higher cost of equity. This is because a lower price means investors are paying less for each dollar of expected future dividends, thus demanding a higher percentage return. Conversely, a higher stock price implies investors are willing to pay more, accepting a lower required rate of return.
3. Expected Dividend Next Year (D1): A higher expected dividend payout increases the numerator in the (D1 / P0) component, thus increasing the cost of equity. Investors receive more cash flow, and their required return on that cash flow is factored in.
4. Market Risk Aversion: General economic conditions and investor sentiment towards the stock market influence the overall required rate of return. During periods of high uncertainty or risk aversion, investors demand higher returns across the board, increasing the cost of equity for all companies.
5. Company-Specific Risk: While the Gordon model doesn’t explicitly include a risk-free rate or beta like CAPM, the P0 reflects market perception of risk. Companies perceived as riskier (e.g., volatile earnings, high debt) tend to have lower stock prices (P0), which, according to the formula, inflates their calculated cost of equity.
6. Inflation Expectations: Inflation erodes the purchasing power of future dividends. Higher expected inflation generally leads investors to demand higher nominal returns, thus increasing the cost of equity. The growth rate ‘g’ and the required return ‘Ke’ implicitly incorporate inflation expectations.
7. Dividend Policy and Reinvestment: The model inherently assumes dividends are paid. Companies choosing to retain earnings for reinvestment rather than paying dividends cannot be directly valued using this specific form of the DDM, though variations exist. The choice of dividend policy impacts the D1 and the perceived stability of future payouts.

Frequently Asked Questions (FAQ)

Q1: What is the main limitation of the Gordon Growth Model?

A1: The primary limitation is its assumption of a constant dividend growth rate in perpetuity, which is unrealistic for most companies. It’s also not suitable for non-dividend-paying stocks or companies with highly variable growth.

Q2: Can the cost of equity be negative using this model?

A2: Mathematically, if the growth rate ‘g’ is greater than the dividend yield (D1/P0), the result could appear low, but ‘g’ must be less than ‘Ke’. A negative Ke is not financially meaningful. If inputs lead to such a result, it indicates the model is misapplied or the inputs are flawed.

Q3: How do I find the expected dividend for next year (D1)?

A3: D1 is typically estimated using historical dividend trends, management guidance, analyst forecasts, and the company’s payout ratio applied to projected earnings per share for the next year.

Q4: What if a company doesn’t pay dividends?

A4: The basic Gordon Growth Model is not directly applicable. In such cases, analysts often use the Capital Asset Pricing Model (CAPM) or other valuation methods that do not rely on current dividends.

Q5: How reliable is the constant growth rate (g)?

A5: Estimating ‘g’ is subjective. It’s often based on the company’s historical growth, industry average growth, or a long-term inflation rate plus a real growth component. It’s crucial that ‘g’ is less than ‘Ke’ and realistic for the company’s stage and industry.

Q6: Should I use the current dividend (D0) or next year’s dividend (D1) in the formula?

A6: You MUST use D1, the expected dividend for the *next* period. If you only have the current dividend (D0), you calculate D1 using the formula: D1 = D0 * (1 + g).

Q7: How does the cost of equity relate to the Weighted Average Cost of Capital (WACC)?

A7: The cost of equity (Ke) is a component of the WACC. WACC represents the company’s blended cost of all capital sources (debt and equity). Ke is specifically the cost associated with the equity portion.

Q8: What is a reasonable growth rate (g) to assume?

A8: A common benchmark for a sustainable long-term growth rate is the expected long-term inflation rate plus the expected long-term real economic growth rate. Often, this falls in the 3% to 6% range for mature economies and stable companies. It should never exceed the cost of equity.