Suppose an investor is considering the purchase of a share of the Utah Mining Company. The stock will pay a $3 dividend a year from today. This dividend is expected to grow at 10 percent per year (g = 10%) for the foreseeable future. The investor thinks that the required return (R) on this stock is 15 percent, given her assessment of Utah Mining’s risk. (We also refer to R as the discount rate of the stock.) What is the price of a share of Utah Mining Company’s stock?

Using the constant growth formula, we calculate the price to be $60:

Today’s price, P₀ , is quite dependent on the value of g. If g had been estimated to be 12.5 percent, the value of the share would have been:

The stock price doubles (from $60 to $120) when g only increases 25 percent (from 10 percent to 12.5 percent). Because of P₀’s dependency on g, one should maintain a healthy sense of skepticism when using this constant growth of dividends model.

Furthermore, note that P₀ is equal to infinity when the growth rate, g, equals the discount rate, R. Because stock prices are never infinite, an estimate of g equal to or greater than R implies an error in estimation. More will be said of this point later.

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$60 = $3 15.10