Question

Stagnant Iron and Steel currently pays a $9.55 annual cash dividend (D₀). They plan to maintain the dividend at this level for the foreseeable future as no future growth is anticipated.
  
If the required rate of return by common stockholders (K_e) is 13 percent, what is the price of the common stock? (Do not round intermediate calculations. Round your answer to 2

Answer 1

Gordon's Growth Model states that Price of a stock is the sum of the Present Values of all the future dividends.

Thus, P0 = D1 / (Ke - g) , where P0 is the current price of the stock ;

D1 = Expected dividend in year 1 = $ 9.55 per share

Ke = Cost of Equity or Required Rate of Return = 13% = 0.13

g = Expected Growth rate of dividends = 0% = 0(As no future growth is anticipated)

So, Price of the stock = 9.55 / (0.13 - 0.00) = 9.55 / 0.13 = 73.46

So, Price of the common stock is $73.46.

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In simple terms we can understand this concept in another way.

As we expect that annual dividends will remain $9.55 each year for forseeable future, without any growth in dividends, and required rate of return is 13%.

So, the price of the stock should be such, which when applied to 13% returns the result as 9.55

So, P x 13% = 9.55

=>P = 9.55 / 13% = 73.46

This is same as dividend capitalisation or dividend growth model or Gordon Growth Model or Dividend Discount Model