Illustration of a Constant Growth Stock (2)

by Maestri

The dividend expected in Year 2 grows to $1.242(1.08) $1.341, but the present value of this dividend falls to $1.043. Continuing, D3 $1.449 and PV(D3) $0.993, and so on. Thus, the expected dividends are growing, but the present value of each successive dividend is declining, because the dividend growth rate (8%) is less than the rate used for discounting the dividends to the present (13.4%).

If we summed the present values of each future dividend, this summation would be the value of the stock, ˆP0. When g is a constant, this summation is equal to D1/(rs g), as shown in Equation 5-2. Therefore, if we extended the lower step function curve in Figure 5-1 on out to infinity and added up the present values of each future dividend, the summation would be identical to the value given by Equation 5-2, $23.00.

Although Equation 5-2 assumes that dividends grow to infinity, most of the value is based on dividends during a relatively short time period. In our example, 70 percent of the value is attributed to the first 25 years, 91 percent to the first 50 years, and 99.4 percent to the first 100 years. So, companies don’t have to live forever for the Gordon growth model to be used.

Taken From : Five-Minute MBA – Corporate Finance

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