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A company whose earnings and dividends are expected to grow at a rate of 3% per year. Next year's dividend is $0.65 per share. The market capitalization rate is 7%.

How do I find the current price of the share?

Gordon's Divident growth model states that: $$P = \frac{D_1}{k-g}$$ where $D_1$ is the price of the dividend in a year's time, $k$ is the market cap rate\required rate of return and $g$ is the growth rate of the dividend.

Now, my initial thoughts were to simply do: $$P = \frac{0.65}{0.07-0.03} = $16.25$$But in the question, it's stated that the company's earnings are also expected to increase by $3\%$ per year too. Does this change anything?

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No - it does not change anything. You have used the same dividend growth rate $g=0.03$ as the earnings growth rate, so implicitly with a constant dividend cover.

If the earnings growth rate and dividend growth rate were different, you might want to use a different valuation model, but that is not the case here.

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