July 7, 2013  

Constant Growth Stock Valuation

Constant Growth Stock Valuation

Stock Valuation is more difficult than Bond Valuation because stocks do not have a finite maturity and the future cash flows, i.e., dividends, are not specified. Therefore, the techniques used for stock valuation must make some assumptions regarding the structure of the dividends.

A constant growth stock is a stock whose dividends are expected to grow at a constant rate in the forseeable future. This condition fits many established firms, which tend to grow over the long run at the same rate as the economy, fairly well. The value of a constant growth stock can be determined using the following equation:

 

where

  • P0 = the stock price at time 0,
  • D0 = the current dividend,
  • D1 = the next dividend (i.e., at time 1),
  • g = the growth rate in dividends, and
  • r = the required return on the stock, and
  • g < r.

Constant Growth Stock Valuation Example

Find the stock price given that the current dividend is $2 per share, dividends are expected to grow at a rate of 6% in the forseeable future, and the required return is 12%.

Solution:

 

 

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Example Problems

Use the following information to determine the stock price.

  

Current Dividend:

$

  

Growth Rate:

 

%

  

Required Return:

 

%

  

Stock Price:

$

  

   

  

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Please see the Constant Growth Stock Exercise for additional example problems which illustrate the calculation of the other variables, i.e., the growth rate, required return, and dividend.

Dividend Yield and Capital Gains Yield

The constant growth stock equation can be rearranged to obtain an expression for the expected return on the stock as follows:

 

When expressed in this manner, it is apparent that the expected return on the stock equals the expected dividend yield plus the expected capital gains yield where the dividend yield and capital gains yield are defined as follows:

 

 

A more general form of the Constant Growth Stock Valuation formula which can be used to find the price of the stock at any period t in the future is given by the following

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