Dividend discount model DDM

Why start a share valuation with dividends?

A share represents ownership in a business. Dividends are one way it transfers cash to owners. DDM converts possible future dividends per share into an amount today. It asks what the assumed cash stream would be worth, not what price the market must eventually pay.

Receiving 100 next year is different from receiving 100 in ten years: waiting has an opportunity cost and the cash is uncertain. Discounting accounts for those differences. Constant-growth DDM simplifies the stream so we can study stable dividend payers; it is not a universal equation for every company.

Separate D₀, D₁, g and r

D₀ is the dividend just paid or for the current year; D₁ is the expected next dividend. With D₀=3 and growth g=3%, the next payment is 3×1.03=3.09. If the input is already D₁=3.09, use it directly rather than growing it again.

Required return r compensates shareholders for the risky cash stream. It is neither a bank deposit rate nor interest promised by the company. Growth g describes the assumed long-term dividend path. Match annual periods and currency, and enter 9% and 3% in the equation as 0.09 and 0.03.

Why must r exceed g?

Dividends grow at g while discounting reduces the value of distant payments. The ratio between consecutive present values is (1+g)/(1+r). Only when r > g do the terms shrink enough for the perpetual sum to have a finite value, allowing D₁/(r−g).

At r=g there is no finite answer, not a zero share price. At r < g, a negative denominator is not a sensible negative stock value. A business growing rapidly for a few years may require a multi-stage model instead of assuming that short-term growth lasts forever.

Work through one consistent set of numbers

Take hypothetical D₀=3, g=3% and r=9%. First obtain D₁=3.09, then calculate 3.09/(0.09−0.03)=51.50. This is value per share; valuing the entire company also requires dealing with the share count and other relevant claims.

Raise only g to 4% and D₁ must become 3.12; value becomes 3.12/(0.09−0.04)=62.40. Alternatively, keep g at 3% but raise required return to 10%: value falls to about 44.14. Higher growth increases future cash and narrows the discount spread; a higher required return demands more compensation and lowers today's acceptable price.

What should you observe in the interaction?

Move the growth control and compare next dividend, value and the curve. The curve steepens as growth approaches r because r−g becomes small. That is greater model sensitivity, not proof that a company suddenly creates a large, certain amount of wealth.

Compare defensible assumptions rather than choosing whichever g justifies a market price. Ask whether dividends are stable, growth is sustainable and payouts represent cash available to shareholders. Repurchases, temporarily absent dividends, changing financing or payout restrictions can make one constant-growth equation inadequate.

Scope and limitations

Requires r > g and g > −100%. Assumes perpetual constant growth and stable dividends; unsuitable for non-dividend or transitional firms. Match currency and annual periods.