Chapter 7, Problem 12PROB

Summary Introduction

The company will pay its first dividend of $3 at the end of 4 years. The dividend would remain the same in the coming years with required rate of 10%

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

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

Special case, when the growth rate of dividend is zero, then

$P_0=\frac{D_1}{r_s}$