Chapter 7, Problem 6PROB

Summary Introduction

WC recently paid a dividend of $2 which is expected to grow continuously at a rate of 5% in perpetuity. The appropriate rate of return on the stock is 12%.

Gordon constant growth model is used to determine the value of a stock. The model assumes that the dividend paid by the company would continue to grow at a constant rate in the foreseeable future. The present value of all these dividends paid till perpetuity is the market or present value of the stock. The model also assumes that the required rate of return of the stock should always be greater than the growth rate, otherwise, the value would become negative and meaningless.

Value of the stock when the dividends are growing at a constant rate is

$\begin{array}{rr}{P}_0& =\frac{D_1}{r_s-g}\hfill \\ & =\frac{D_0\left(1+g\right)}{r_s-g}\hfill \\ & where,\hfill \\ D_1& =\text{dividend paid next year}\hfill \\ D_0& =\text{dividend paid this year}\hfill \\ {\text{r}}_s& =\text{required rate of return}\hfill \\ g& =\text{growth rate of dividend in perpetuity}\hfill \end{array}$