How does the Gordon Growth Model work for valuing a stock? What happens if g is close to r?

The Gordon Growth Model (GGM) is one of the foundational valuation tools in the CFA curriculum. You're right that it looks simple, but the exam tests whether you truly understand its assumptions and limitations. **The Formula:** **V_0 = D_1 / (r - g)** Where: - V_0 = intrinsic value of the stock today - D_1 = expected dividend next year - r = required rate of return (cost of equity) - g = constant growth rate of dividends (forever) **Worked Example:** Bramblewood Industries just paid a dividend (D_0) of $2.80 per share. Dividends are expected to grow at 4% per year indefinitely. The required return on the stock is 10%. **Step 1 — Calculate D_1:** D_1 = D_0 x (1 + g) = $2.80 x 1.04 = **$2.912** **Step 2 — Apply the GGM:** V_0 = $2.912 / (0.10 - 0.04) = $2.912 / 0.06 = **$48.53** If the stock is trading at $42.00, it appears **undervalued** by $6.53 per the GGM. **What Happens When g Approaches r?** This is where the model breaks down. As g approaches r, the denominator (r - g) approaches zero, and the value shoots toward infinity. For example: | g | r - g | V_0 | |-----|-------|-------| | 4% | 6% | $48.53 | | 7% | 3% | $99.87 | | 9% | 1% | $304.64 | | 9.9% | 0.1% | $3,080.00 | This is economically nonsensical. **No company can grow dividends at a rate equal to or exceeding the required return forever.** If g >= r, the model is undefined and should not be used. **Key Assumptions and Limitations:** 1. **Constant growth forever** — Unrealistic for high-growth companies. Use a **two-stage DDM** when growth is expected to slow over time. 2. **g must be less than r** — A mathematical requirement. The sustainable growth rate is typically bounded by long-run nominal GDP growth (around 4-5%). 3. **Company must pay dividends** — For non-dividend-paying stocks, use free cash flow models or residual income models instead. 4. **Sensitivity to inputs** — Small changes in g or r cause large swings in value. The exam may test this by asking you to recalculate value with a 1% change in growth rate. **When to Use GGM vs Multi-Stage DDM:** - **GGM**: Mature, stable companies with predictable dividend growth (utilities, consumer staples) - **Two-stage DDM**: Companies with a high-growth phase followed by stable growth (tech companies transitioning to maturity) For extensive practice with dividend discount models and other equity valuation methods, explore our CFA Level I question bank on AcadiFi.