 # The Required Rate of Return the 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

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

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

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