Question

Frazzled Inc. paid a dividend of $3.00 earlier today. Your stockbroker believes that the stock will sell for $52 in three years. This price is based on her belief that the stock's dividends will grow at a rate of 10% for the next three years and that the appropriate discount rate for this stock is 15%. Suppose your stockbroker tells you that she determined that the stock would sell for $52 in three years by using the constant growth model of stock valuation based on the dividends from year four forward. What constant dividend growth rate must she be assuming from year three forward?

Answer 1

Dividend in year 3 = Dividend 0*(1+Growth rate)^3

= 3*(1.1)^3

= $3.993

Let the constant growth rate after year 3 be x

Stock Price at the end of year 3 = Dividend in year 4/(required return - constant growth rate)

52 = 3.993*(1+x)/(15%-x)

7.8 - 52x = 3.993 + 3.993x

3.807 = 55.993x

x = 6.799%

i.e. 6.80%

Hence, the constant growth rate used is 6.80%