The Required Rate of Return the Gordon Growth Model and the H-model

Given all the inputs to a dividend discount model (DDM) except the required return, the IRR can be calculated and used as a substitute for the required rate of return. This IRR can be interpreted as the expected return on the issue implied by the market price.

The Gordon Growth Model

Using the Gordon growth model, the required rate of return can be calculated as:

$$\text{r}=\frac{\text{D}_{1}}{\text{P}_{0}}+\text{g}$$

Example: Estimating the Required Rate of Return

If a security has a current dividend of $1.50, a current price of $25, and an expected growth rate of 4%, then the required rate of return would be:

$$\begin{align*}\text{r}&=\frac{1.50(1.04)}{25}+0.04\\&=10.24\%\end{align*}$$

The H-model

Using the H-model, the required rate of return can be calculated as:

$$\text{r}=\bigg(\frac{\text{D}_{0}}{\text{P}_{0}}\bigg)[(1+\text{g}_{\text{L}})+\text{H}(\text{g}_{S}-\text{g}_{\text{L}})]+\text{g}_{L}$$

Example: Estimating the Required Rate of Return

If a security has a dividend of $1.50, a current price of $25, and an expected short-term growth rate of 10% declining linearly over 10 years to 6%, then the expected rate of return would be:

$$\begin{align*}\text{r}&=\bigg(\frac{1.50}{25}\bigg)[(1.06)+5(0.04)]+0.06\\&=13.56\%\end{align*}$$

Question

For a security with an expected dividend of $2.50, a current price of $38, and an expected growth rate of 5%, the required rate of return would be closest to:

1. 9.5%.
2. 11.58%.
3. 15.55%.

Solution 

The correct answer is B.

$$\begin{align*}\text{r}&=\frac{\text{D}_{1}}{\text{P}_{0}}+\text{g}\\ \\&=\frac{2.50}{38}+0.05\\ \\&=11.58\%\end{align*}$$

Reading 23: Discounted Dividend Valuation

LOS 23 (n) Estimate a required return based on any DDM, including the Gordon growth model and the H-model.