Chapter 14, Problem 14.2CTF

A firm has paid dividends of $1.02, $1.10, $1.25, and $1.35 over the past 4 years, respectively. What is the average dividend growth rate?

Summary Introduction

To determine: The dividend growth rate.

Introduction:

Dividend refers to the return on the equity capital. Dividend growth rate refers to the rate at which the dividend grew for a certain period.

Answer to Problem 14.2CTF

The “average dividend growth rate” is 9.83 percent.

Explanation of Solution

Given information:

A firm paid dividends amounting to $1.02 in Year 1, $1.10 in Year 2, $1.25 in Year 3, and $1.35 in Year 4.

The formula to compute the percentage change in dividend each year:

$\begin{array}{l}\text{Percentage change in dividend}\\ \text{in the current year}\end{array}\}=\frac{\text{Current dividend}-\text{Previous year dividend}}{\text{Previous year dividend}}\times 100$

The formula to calculate the “average dividend growth rate”:

$\begin{array}{l}\text{Average}\\ \text{dividend}\\ \text{growth rate}\end{array}\}=\frac{\left(\begin{array}{l}\text{Percentage change}\\ \text{in dividend}\\ \text{for the first year}\end{array}\right)+\left(\begin{array}{l}\text{Percentage change}\\ \text{in dividend}\\ \text{for the second year}\end{array}\right)+\mathrm{\dots }+\left(\begin{array}{l}\text{Percentage change}\\ \text{in dividend}\\ \text{for the }{N}^{th}\text{ year}\end{array}\right)}{\text{Number of years}}$

Compute the percentage change in dividend for Year 2:

$\begin{array}{c}\begin{array}{l}\text{Percentage change}\\ \text{in dividend}\\ \text{in Year 2}\end{array}\}=\frac{\text{Dividend in Year 2 }-\text{Dividend in Year 1}}{\text{Dividend in Year 1}}\times 100\\ =\frac{\$1.10-\$1.02}{\$1.02}\times 100\\ =\frac{\$0.08}{\$1.02}\times 100\\ =7.84\%\end{array}$

Hence, the percentage change in dividend for Year 2 is 7.84 percent.

Compute the percentage change in dividend for Year 3:

$\begin{array}{c}\begin{array}{l}\text{Percentage change}\\ \text{in dividend}\\ \text{in Year 3}\end{array}\}=\frac{\text{Dividend in Year 3 }-\text{Dividend in Year 2}}{\text{Dividend in Year 2}}\times 100\\ =\frac{\$1.25-\$1.10}{\$1.10}\times 100\\ =\frac{\$0.15}{\$1.10}\times 100\\ =13.64\%\end{array}$

Hence, the percentage change in dividend for Year 3 is 13.64 percent.

Compute the percentage change in dividend for Year 4:

$\begin{array}{c}\begin{array}{l}\text{Percentage change}\\ \text{in dividend}\\ \text{in Year 4}\end{array}\}=\frac{\text{Dividend in Year 4 }-\text{Dividend in Year 3}}{\text{Dividend in Year 3}}\times 100\\ =\frac{\$1.35-\$1.25}{\$1.25}\times 100\\ =\frac{\$0.10}{\$1.25}\times 100\\ =8\%\end{array}$

Hence, the percentage change in dividend for Year 4 is 8 percent.

Compute the “average dividend growth rate”:

$\begin{array}{c}\begin{array}{l}\text{Average}\\ \text{dividend}\\ \text{growth rate}\end{array}\}=\frac{\left(\begin{array}{l}\text{Percentage change}\\ \text{in dividend}\\ \text{for Year 2}\end{array}\right)+\left(\begin{array}{l}\text{Percentage change}\\ \text{in dividend}\\ \text{for Year 3}\end{array}\right)+\left(\begin{array}{l}\text{Percentage change}\\ \text{in dividend}\\ \text{for Year 4}\end{array}\right)}{\text{3}}\\ =\frac{7.84\%+13.64\%+8\%}{3}\\ =\frac{29.48\%}{3}\\ =9.83\%\end{array}$

Hence, the “average dividend growth rate” is 9.83 percent.