Question

1. company is expected to pay its first dividend in the amount of $2 a share 7 years from today. The dividend in year 8 will be $2.25 a share and the dividend in year 9 will be $2.50 a share, after which a constant annual growth in dividends is expected. The appropriate annual discount rate of company’s stock is 11%. If the company’s stock is selling for $38.10 a share, what is the annual growth rate expected by investors in the company’s dividends after year 9? (Use 5 decimals in calculations to measure the growth rate more precisely.) Please show all work.

Answer 1

Given the information , growth rate after year 9 can be found as

[Dividend of year 7 x PVIF(11%,7)] +[ Dividend of year 8 x PVIF(11%,8)] + [Dividend of year 9 x PVIF(11%,9)] + [Dividend of year 9(1+g)/Ke- g x PVIF(11%,9)] = 38.1

Here g = growth rate

[2 x 1/(1.11)^7 ] + [2.25 x 1/(1.11)^8] + [ 2.5 x 1/(1.1)^9 ] +[ 2.5(1+g)/11%-g x 1/(1.1)^9] = 38.1

=[ 2 x 0.48166] + [2.25 x 0.43392] + [2.5 x 0.39092] +[ 2.5(1+g)/11%-g x 0.39092] =38.1

=0.96332 + 0.97633 + 0.97731 +[ 2.5(1+g)/11%-g x 0.39092] =38.1

=2.91696 + [ 2.5(1+g)/11%-g x 0.39092] =38.1

= [ 2.5(1+g)/11%-g x 0.39092] = 35.18303

=2.5 +2.5g/11%-g x 0.39092 = 35.18303

=0.9773 + 0.9773g / 11% -g =35.18303

= 0.9773 + 0.9773g = 35.18303(11%-g)

0.9773 + 0.9773g = 3.870133 - 35.18303g

=36.16033g = 2.89283

g = 8.00001%

i.e 8%