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## 1.3.6 Constantly Growing Perpetuity

What if we expect that future returns will grow, with inflation and as an investment progresses? If returns grow at a constant rate (g), the DCF formula produces one of the most often-used formulas in stock valuation -- known as the "Gordon-Shapiro dividend discount model" or the "Gordon model."

 P0 =D0×(1+g)1 / (1+i)1 +D0×(1+g)2 / (1+i)2 + ... + D0×(1+g)inf / (1+i)inf P0 = D1 / (i - g) or P0 = D0 (1 +g) / (i - g) P0 present value of common stock (with constant growth returns) D0 most recent per-share dividend D1 per-share dividend after one period of growth [D1 = D0 (1 + g)] i required return (discount rate) for each year t g rate of growth inf infinite time period

Notice that this model makes heroic (assuredly wrong) assumptions about the flat continuity of growth and that extrapolation from past earnings reflects likely future earnings. But at least it's a start.

Example

Company is growing. It pays most of its earnings as dividends, but retains some earnings for future growth. The practice has worked well, as its history of growth suggests.

What is the value of Company stock, based on dividend returns? (More>>)

 Year Dividend/Share 1 1.00 2 1.06 3 1.15 4 1.25 5 1.36 6 1.44 7 1.59

 1.3.5 Present Value of a Perpetuity 1.4.0 Legal applications