Question

A company has announced the growth rate of its dividend going forward will be 2% annually forever. The dividend in year 5 will be $3.00. The discount rate on the stock is 8%. What will the dividend be in year 14?

Answer 1

Solution

Given the growth rate of dividend =2%

5th-year dividend =$3

Therefore dividend paid at the end of first year can be found by discounting $3 @ 2%

Discounting formula= Amount/(1+r)^n

= 3/(1+.02)^4

=2.771536

Now dividend paid at end of 14th year can be found by compounding formula @2%= Amount*(1+r)^n

where the amount is the dividend paid at the end of the first year

This dividend will again grow by 2% every year 13 times

Therfore dividend at end of 14 year =2.771536*(1.02^13)

=$3.585