Stock Valuation: Dividend Discount Model for Exam FM

Dividend Discount Model

The value of a stock is the present value of all future dividends: P = sum of D_t / (1+r)^t for t = 1, 2, 3, ..., where r is the required rate of return. If dividends grow at a constant rate g forever (the Gordon Growth Model): P = D_1 / (r - g), where D_1 is the next dividend and r > g. This is a perpetuity-due growing at rate g.

Example: A stock pays a dividend of $2 next year, growing at 3% per year. If the required return is 10%, the stock value is 2 / (0.10 - 0.03) = $28.57.

Multi-Stage Growth

When dividend growth is not constant, use a multi-stage model. Typically, dividends grow at a high rate for a finite period, then switch to a sustainable long-term rate. Value = PV of high-growth dividends + PV of the terminal value, where the terminal value at the switch point uses the Gordon formula with the long-term growth rate.

Example: D_1 = $3, growing at 15% for 3 years, then 4% forever. At r = 12%: compute D_1, D_2, D_3, D_4, find the terminal value at time 3 as D_4/(r - g) = D_3*1.04/0.08, and discount everything to time 0.

Exam FM Applications

Exam FM tests the basic Gordon model, finding the implied growth rate or required return, and comparing stock prices under different assumptions. Remember that the model assumes dividends are the only cash flow to shareholders. The earnings growth rate g can be estimated as g = retention ratio * return on equity. If a stock pays no dividends, the DDM does not directly apply.