ABSTRACT

But here we can define Div(t +1) ≡ n(t)div(t +1) to be the total value of the dividends paid out by the firm at time t + 1 and V (t) ≡ n(t)P(t) to be the overall market value of the firm’s equity at time t. Using these definitions it follows that the return on equity over the period from time t until time t + 1 can be restated as

r(t + 1) = Div(t + 1)+ n(t)P(t + 1)−V (t) V (t)

= Div(t + 1)+ n(t)P(t + 1) V (t)

− 1

or

V (t) = Div(t + 1)+ n(t)P(t + 1) 1+ r(t + 1)

This result says that themarket valueV (t) of the firm’s equity at time t is given by discounting the market value of its shares at time t + 1,

n(t)P(t + 1) 1+ r(t + 1)

and adding the discounted value of any dividends that will be paid at time t + 1, Div(t + 1) 1+ r(t + 1) =

n(t)div(t + 1) 1+ r(t + 1)

Note that this equation, which is often referred to as the Hamilton-Jacobi-Bellman equation, seems to suggest that a firm’s dividend policy does have important implications for the value of the firm’s equity, since the total dividend paid by the firm, Div(t + 1), is an instrumental variable on the right-hand side of the equation. We now show, however, that this is not the case.