Question

What is the annual growth rate of dividends for a particular stock over the years 2004-2009?
2004: $0.14
2005: $0.15
2006: $0.17
2007: $0.17
2008: $0.19
2009: $0.22

Answer 1

Since we are trying to determine the annual growth rate I attempted to use the geometric mean
\[ ( 1.14*1.15*1.17*1.17*1.19*1.22)^{\frac{1}{6}}-1\]

Answer 2

But the answer in the back of the book goes as follows:
\[ \left (\frac{.22}{.14} \right) ^{\frac{1}{5}}-1\]

Answer 3

@dan815

Answer 4

Like I get what they did ...
\[\left ( \frac{ \text{ End period }}{ \text{ Begin period }} \right )\]
Which basically gives you the return over 5 years and then you take the quad root

Answer 5

ohhh and in my equation i was basically determining my annual rate of return (basically my average dividend with dividends reinvested )on an investment if I received these amt of dividends over the 6 years

Answer 6

Basically I was doing annual growth rate of investment instead of annual growth rate of dividends

Answer 7

Hmmm sorry I don't know really much about financial math. I don't know if this helps, cause I'm not really sure what your question is, but it is kind of a combination of what you did and what the answer is if that makes more sense unless you already knew this. \[\left( \frac{.15}{.14}* \frac{.17}{.15} *\frac{.17}{.17} *\frac{.19}{.17}*\frac{.22}{.19}\right)^{1/5}-1\] I'm trying to get into this kind of math though, so if you can explain anything to me any time that would be nice

Answer 8

Hey I guess that is another way of looking at it

Answer 9

The esteemed @tkhunny

Answer 10

2004: $0.14 2005: $0.15 2006: $0.17

First Growth Rate (0.15 - 0.14) / 0.14 = 0.0714%
Second Growth Rate (0.17 - 0.15) / 0.15 = 0.1333%

Growth Rate for 1st and 2nd years combined

[1.0714 * 1.1333]^(½) - 1 = 0.1019

Growth Rate for 1st and 2nd years combined

(0.17 / 0.14)^(½) - 1 = 0.1019

Take your pick, but do it carefully.

Answer 11

Okkk i get ittt nowwwww
Thank you sooo much @tkhunny