# The Implied Dividend Growth Rate

Different growth rate assumptions may explain the differences between the estimated values of a share and the actual market value. Given the price, the expected dividend, and the required rate of return, the dividend growth rate reflected in the price can be inferred using the Gordon growth model. The plausibility of the growth rate can then be evaluated.

#### Example: The Implied Dividend Growth Rate

Suppose a company’s current dividend is $3.00 and the required rate of return is 11%. The dividend growth rate that would be required to justify a share market price of$45 would be:

\begin{align*}\text{V}_0&= \frac{\text{D}_0(1+\text{g})}{(\text{r}-\text{g})}\\ \\45&=\frac{3(1+\text{g})}{(11\%-\text{g})}\\ \\4.95-45\text{g}&=3+3\text{g}\\ \\48\text{g}&=1.95\\\ \\text{g}&=4.06\%\end{align*}

## Question

Consider a company with a required rate of return of 12% and a share market price of $30. If the next period’s dividend is expected to be$2.00, the dividend growth rate is closest to:

1. 33%.
2. 25%.
3. 50%.

#### Solution

\begin{align*} \text{V}_0&= \frac{\text{D}_0(1+\text{g})}{(\text{r}-\text{g})} \\ \\ 30&=\frac{2.00}{(12\%-\text{g})} \\ \\3.6-30\text{g}&= 2\\ \\30\text{g}&=1.6\\ \\\text{g}&=5.33\%\end{align*}

LOS 23 (e) Calculate and interpret the implied growth rate of dividends using the Gordon growth model and current stock price.

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