Highway Express has paid annual dividends of $1.32, $1.33, $1.38, $1.40, and $1.42 over the past five years, respectively. What is the average dividend growth rate?
Multiple Choice
2.39 percent
2.47 percent
1.85 percent
1.98 percent
2.16 percent
The correct answer and explanation is :
To determine the average dividend growth rate for Highway Express over the past five years, we can apply the Compound Annual Growth Rate (CAGR) formula. This method provides a consistent rate at which dividends have grown annually over the period, smoothing out fluctuations.
Step 1: Understand the CAGR Formula
The CAGR formula is expressed as:
[ \text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{n}} – 1 ]
Where:
- Ending Value is the dividend at the end of the period.
- Beginning Value is the dividend at the start of the period.
- n is the number of years over which the growth occurs.
Step 2: Apply the Given Data
The dividends over the past five years are:
- Year 1: $1.32
- Year 2: $1.33
- Year 3: $1.38
- Year 4: $1.40
- Year 5: $1.42
Here, the Beginning Value is $1.32 (Year 1 dividend), and the Ending Value is $1.42 (Year 5 dividend). The number of years (n) is 4, as the growth occurs over four intervals between the five data points.
Step 3: Calculate the CAGR
Using the CAGR formula:
[ \text{CAGR} = \left( \frac{1.42}{1.32} \right)^{\frac{1}{4}} – 1 ]
First, calculate the ratio:
[ \frac{1.42}{1.32} \approx 1.07576 ]
Then, raise this ratio to the power of ( \frac{1}{4} ):
[ 1.07576^{0.25} \approx 1.0185 ]
Subtract 1 to find the growth rate:
[ 1.0185 – 1 = 0.0185 ]
Convert this decimal to a percentage:
[ 0.0185 \times 100 = 1.85\% ]
Conclusion
The average annual dividend growth rate for Highway Express over the past five years is approximately 1.85%.