Final answer:
The arithmetic average growth rate and the geometric average growth rate in earnings per share between 1989 and 1994 can be calculated using different formulas. The geometric average growth rate is generally considered more reliable because it takes into account the compounding effect of growth over multiple years. Linear and log-linear growth models can also be used to estimate the growth rate.
Step-by-step explanation:
The arithmetic average growth rate in earnings per share between 1989 and 1994 can be calculated by taking the average of the annual growth rates. We can find the annual growth rate by dividing the difference in earnings per share between two consecutive years by the initial earnings per share, and then multiplying by 100. For example, for 1989 to 1990, the growth rate would be [(1.42 - 1.28) / 1.28] * 100 = 10.94%. By calculating the growth rates for each year and then averaging them, we can find the arithmetic average growth rate.
The geometric average growth rate in earnings per share can be calculated using the formula [(EPSt_final / EPSt_initial)^(1/n) - 1] * 100, where EPSt_final is the earnings per share at the end of the period, EPSt_initial is the earnings per share at the beginning of the period, and n is the number of years. Using this formula, we can calculate the geometric average growth rate for the given data.
The arithmetic average growth rate and geometric average growth rate may be different due to the compounding effect of growth. The arithmetic average growth rate assumes equal growth from year to year, while the geometric average growth rate takes into account the compounding effect of growth over multiple years. The geometric average growth rate is generally considered more reliable because it captures the compounding effect and provides a more accurate representation of the overall growth over the period.
To estimate the growth rate using a linear growth model, we can calculate the slope of a linear regression line that best fits the data points representing the earnings per share over the years. This slope represents the average annual growth rate.
To estimate the growth rate using a log-linear growth model, we can take the natural logarithm of the earnings per share values and then calculate the slope of a linear regression line on the transformed data. The slope represents the average annual growth rate in this case.