Why is the Value Estimated from the Constant Dividend Growth Model not an Equilibrium Value?

Abstract

For dividend discount models, the intrinsic value of stock is estimated by discounting all the future dividends of the stock. In the simplest assumption where growth is constant forever, the Constant Dividend Growth Model formula is expressed as P = D1 / (k-g). The premise is that the firm will pay future dividend that will grow at a constant rate.

In this paper, we show that the price generated by this traditional formula is not stable if ROE is not equal to k. In the long run where capital can be varied, the company’s ROE should be equal to k. Otherwise, firms will have the incentive to boost share value by increasing or reducing capital accordingly. The long run equilibrium state is attained when the return on equity is equal to the required return (k = ROE). In such case, the constant dividend growth model can be simplified to: V = EPS1 / k. Only in the condition where k = ROE would the price yielded by the traditional dividend growth model is stable. Interestingly, the derived valuation formula for the long run equilibrium condition is based on only EPS and required return, which means that the model can also be applied to firms which pay no dividend.

Keywords: Dividend Discount Model, Constant Growth

JEL Classification: G12