1. The problem is to write the formula for the true multistage H model used to determine the fair value of a stock. 2. The H model is a dividend discount model that assumes a gradual change in the growth rate of dividends from a higher initial growth rate to a stable long-term growth rate. 3. The formula for the true multistage H model is: $$P_0 = \frac{D_0 (1 + g_L)}{r - g_L} + \frac{D_0 H (g_S - g_L)}{r - g_L}$$ where: - $P_0$ is the fair value of the stock today. - $D_0$ is the most recent dividend paid. - $g_S$ is the initial short-term growth rate. - $g_L$ is the long-term stable growth rate. - $r$ is the required rate of return. - $H$ is half the length of the high growth period (in years). 4. Explanation: - The first term, $\frac{D_0 (1 + g_L)}{r - g_L}$, represents the value of the stock assuming dividends grow at the long-term rate $g_L$ indefinitely. - The second term, $\frac{D_0 H (g_S - g_L)}{r - g_L}$, adjusts for the higher growth rate $g_S$ during the initial high growth period, scaled by $H$. 5. This model captures the transition from a high growth phase to a stable growth phase more realistically than a simple constant growth model. 6. Important rules: - The required rate of return $r$ must be greater than the long-term growth rate $g_L$ to avoid division by zero or negative valuation. - The growth rates $g_S$ and $g_L$ are expressed as decimals (e.g., 0.10 for 10%). This formula helps investors estimate the fair value of a stock considering changing growth rates over time.