American Nanotech Inc began paying dividends for the first t

American Nanotech, Inc. began paying dividends for the first time three years ago and just paid a dividend of $5 today. You epect that dividend to grow by 25% for the upcoming two years, until competitive forces will force that grow rate down to a constant 4%, the long-term growth rate of the U.S. economy. If the expected rate of return for high-tech, nano-technology firms is 15%, what\'s the fair price of American Nanotech\'s stock? A) $53.75 B) $62.78 C) $78.47 D) $86.53 E) $67.19

Solution

D1=(5*1.25)=$6.25

D2=(6.25*1.25)=$7.8125

Value after year 2=(D2*Growth rate)/(Expected rate of return-Growth rate)

=(7.8125*1.04)/(0.15-0.04)=$73.863636(Approx)

Hence fair price=Future dividends*Present value of discounting factor(15%,time period)

=6.25/1.15+7.8125/1.15^2+73.863636/1.15^2

=$67.19(Approx).