Chapter 7, Problem 15PROB

Summary Introduction

The company FF will pay $1.50 at the end of this year, $2 at the end of year 2, post which it will increase its dividend by 5% indefinitely. Required rate of return on the stock is 11%.

Non-Constant Dividend Growth Model

Non-constant growth model assumes that the company pay dividends based on its growth stage. According to the model, different amounts of dividends are paid in the initial years and then at some point of time they enter a phase with constant dividend growth model. Therefore, for the period in which the dividends paid are varying, present value of each period is calculated. Constant growth model is applied when the dividends start growing at a constant rate later.

Stock price for non-constant growth model can be computed as follows:

Step 1

Find dividends for the non-constant growth period and discount them to the present value

Step 2

Compute the dividend at the start of the constant growth period and then using constant growth model, calculate the horizontal value of the stock at the end of the non-constant growth period.

Step 3

Find the present value of this horizontal stock price

Step 4

Add the present value of all the dividends and the present value of the horizontal price, to determine the current stock value

$\begin{array}{rr}{P}_0& ={\displaystyle \sum _{time=1}^n\frac{D_n}{{(1+r_s)}^n}+}\frac{P_t}{{\left(1+r_s\right)}^t}\hfill \\ where,\\ D& =\text{dividends paid in the non-constant period}\hfill \\ r_s& =\text{ required rate of return}\hfill \\ P_t& =\text{ Horizontal price of the stock}\hfill \end{array}$

$\begin{array}{rr}{P}_t& =\frac{D_t\left(1+g\right)}{r_s-g}\hfill \\ where\\ D_t& =\text{dividend at the end of non-constant growth period}\hfill \\ g& =\text{growth rate of dividend}\hfill \end{array}$