Work out the value of a common share with the dividend discount model (DDM) over one holding period and over several, and explain the result
The idea
A share is worth the present value of the dividends received while it is held plus the present value of the expected sale price, discounted at the required return on equity. For one period, value equals (D1 + P1) ÷ (1 + r). For n periods, add each dividend Dt ÷ (1 + r)ᵗ and then Pn ÷ (1 + r)ⁿ. Because the sale price itself reflects the dividends expected after the sale, extending the horizon indefinitely leaves value equal to the present value of all future dividends. Two errors are common: discounting the sale price for one period fewer than the final dividend it arrives with, and using the dividend just paid, D0, where the first expected dividend, D1, belongs.
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