Equity Valuation
Dividend discount models
The Gordon growth model, P0 = D1/(r - g), requires r > g and a growth rate sustainable forever, where g = retention ratio x ROE. Two-stage and H-models relax constant growth. Multiples derive from the same fundamentals: justified P/E = payout ratio/(r - g); justified P/B = (ROE - g)/(r - g).
Free cash flow and residual income
FCFF is discounted at WACC and FCFE at the cost of equity. Residual income, V0 = B0 + the present value of (ROE - r) x B(t-1), is useful when cash flows are negative or uncertain and is less sensitive to terminal assumptions; apply a persistence factor to terminal residual income.
Traps
- Use D1, not D0, in the Gordon model.
- Terminal value timing: a horizon multiple or Gordon value is measured at the forecast horizon, then discounted back.
- A higher payout does not raise value if it sacrifices growth.
- Residual income requires clean surplus accounting.
- Private company values need discounts for lack of control and lack of marketability.
Worked example
A stock pays D0 = $2.00, with g = 4% and r = 9%. D1 = $2.08 and P0 = 2.08/(0.09 - 0.04) = $41.60. If the market price is $38, the implied return exceeds 9%, all else equal, and the share screens as undervalued.
For the H-model, add D0 x H x (g_short - g_long)/(r - g_long) to the stable-growth value. Rule of thumb: every model is a present value of future cash flows, so check that long-run growth is funded by the return on new investment and does not exceed the required return.