# Understanding Walter's Dividend Policy Model

I'm trying to understand the justification for the mathematical formulation of the Walter model (1956), which provides an equation for the price of a stock based on present value of dividends and reinvestment of retained earnings. The equation is given by

$$P = \frac{D}{K} + \dfrac{\frac{R(E-D)}{K}}{K}$$,

where $$P$$ is the price, $$D$$ is the dividend, $$R$$ is the return on additional investment, $$E$$ is earnings, and $$K$$ is the cost of equity (i.e. required return).

I understand that $$D/K$$ reflects the present value of an infinite perpetuity. I also understand that $$R(E-D)$$ is the income obtained from reinvestment of retained earnings.

What I do not understand is why we end up with $$K^2$$ in the denominator of the second term. It seems to me that $$R(E-D)/K$$ is the present value of a stream of reinvestment income paid out to shareholders - this what I thought we wanted.

Dividing by $$K$$ suggests that shareholders are paid a stream of present values. This is specifically what I do not understand.

## 1 Answer

Say you have a company that has a 25% payout rate on EPS 1, and can invest retained earnings at say 10%. So every year, it has DPS 0.25 and retained 0.75

The D/K part is the NPV of receiving the 0.25 dividend in perpetuity, discounted by K.

Every year the 0.75 is then retained and invested. At 10% returns, that is 0.075 in perpetuity for that year's vintage, which has an NPV of 0.75/K.

But this 0.75/K is just a single year figure.

The company retains and invests the same 0.75 at 10% forever = worth 0.75/K every year. This is worth 0.75/K every year. In perpetuity, this is worth (0.75/K)/K, which is where you get your square.