Valuing shares with dividend discount models

In short

• Equity has no maturity, so its value is the PV of expected dividends forever, discounted at the required return r.
• Constant dividend (e.g. preferred stock): $PV = D/r$.
• Constant growth (Gordon): $PV_0 = D_1/(r-g)$ with $D_1 = D_0(1+g)$. It needs $r > g$.
• Changing growth (two-stage): discount each high-growth dividend, then add the terminal value $D_{n+1}/(r-g_L)$ discounted n periods.
• Value rises with expected growth and falls with the required return.