Question

Brown Inc.'s stock currently sells for $35.25 per share. The dividend is projected to increase at a constant rate of 4.50% per year. The required rate of return on the stock, r , is 11.50%. What is the stock's expected price 5 years from now?

Answer 1

Expected Price of Stock = Expected Dividend / (Rate of return% - Dividend growth rate%)

Stock Price = 35.25

Here we need to calculate expected dividend at the end of 5th Year

Expected dividend for current year = Stock price (Rate of return% - Dividend growth rate%)

   = 35.25 (11.50% - 4.50%)

   = 35.25 * 7% = $2.467

Expected Dividend for 1st Year = Previous year dividend + Growth rate * Previous year dividend

= 2.467 + 4.50% * 2.467

= 2.467 + 0.111 = $ 2.578

Expected Dividend for 2nd Year = 2.578 + 4.50% * 2.578

   = 2.578 + 0.116 = $ 2.694

Expected Dividend for 3rd Year = 2.694 + 4.50% * 2.694

   = 2.694 + 0.121 = $ 2.815

Expected Dividend for 4th Year = 2.815 + 4.50% * 2.815

= 2.815 + 0.126    = $ 2.942

Expected Dividend for 5th Year = 2.942 + 4.50% * 2.942

= 2.942 + 0.132    = $ 3.074

Stock Price after 5 years = Expected Dividend / (Rate of return% - Dividend growth rate%)

= 3.074/11.50% - 4.50%

   = 3.074/7%

   = 43.91

Stock Price after 5 years comes out to be $43.91