The cash flows a dividend model values

DDM values a share by discounting expected dividends. It does not say dividends are a shareholder's only way to receive cash. If repurchases dominate distributions or dividends differ materially from payout capacity, dividends alone may not represent the business well. CFA's valuation explanation identifies choosing the cash-flow definition as a starting point.

The Gordon formula requires r > g

In P 0 = D 1/(r −g), D 1 is next year's expected dividend per share, r is the required equity return and g is perpetual constant dividend growth. Match annual dividends with annual rates, the same currency and consistent nominal or real assumptions. The infinite series converges only if r > g. When r = g the denominator is zero; when r < g a negative result signals failure of the model's conditions, not an undervalued stock.

Aswath Damodaran's lecture describes stable growth and leverage and dividends approximating free cash flow to equity as suitable conditions. Its historical growth estimates and company prices are not current forecasts. If stable growth starts only after a high-growth phase, forecast the earlier dividends separately and discount the stable-phase value back to today.

Change the next dividend and assumptions explicitly

Illustrative inputs: today's dividend D 0 = 2 units, g = 3% and r = 8%. D 1 = 2×1.03 = 2.06, so P 0 = 2.06/(0.08−0.03) = 41.20. Putting D 0 directly in the numerator instead gives 40.00.

Keeping D 0 and g unchanged but raising r to 9% gives 34.33. Keeping D 0 and r unchanged but raising g to 4% changes D 1 to 2.08 and value to 52.00. In the second comparison both next dividend and denominator change. These are sensitivities under stated inputs, not obtainable market prices. A small denominator magnifies input error; compare an assumption range rather than treating one estimate as certain.

Retention times ROE is a conditional consistency check

With b = 1−payout ratio, g ≈ b×ROE checks growth consistency under stable payout, ROE and capital structure, with retained earnings reinvested at the assumed profitability. If b = 30% and ROE = 10%, the result is 3%; historical ROE does not guarantee the return on new investment. Separate buyback-driven equity shrinkage and one-off profits first. This relation alone proves neither future dividend growth nor returns above an external hurdle rate.