Ashley owns stock in a company which has consistently paid a growing dividend over the last five years. The first year Ashley owned the stock (year 0), she received $1.71 per share and 5 years later, she received $2.08 per share. What is the compound annual growth rate of the dividends over the last five years?

Question

BlackTom AI · Accepted Answer

Let's unpack the problem step by step and keep track of the numbers carefully.
First, identify the dividend values at the start and end of the five-year period: $1.71 per share in year 0 and $2.08 per share in year 5.
Next, compute the total growth factor over the five years: growth factor = final dividend / initial dividend = 2.08 / 1.71 ≈ 1.2164.
To convert this into a compound annual growth rate (CAGR), we take the fifth root of the growth factor (since there are 5 years) and then subtract 1: CAGR = (1.2164)^(1/5) − 1.
Calculating the fifth root, we get approximately 1.0399, which corresponds to a CAGR of about 0.0399, i.e., 3.99%.
Rounding to a reasonable accuracy for a multiple-choice choice, this is about 4.0% per year.
Note on the given data: the problem provides a single correct numerical choice (4.0 percent) and, in this instance, there are no alternative distractor options listed to evaluate. The essential check is that the dividend growth is evaluated as a geometric (compound) growth over five years, not a simple average; the CAGR formula (final/initial)^(1/years) − 1 is the appropriate method here.
If a student were tempted to use a simple average growth ((2.08 − 1.71)/5) or linear growth, that would misrepresent compounding, which is why CAGR is the correct approach for this question.

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