Question

last year apricot angles inc had earning per share of $1.20 and its growth rate during the prior 5 years was 7.75% per year. if the growth rate is maintained how many years would it take for AA EPS to reach $4.85 per share?

Answer 1

To find the number of years it would take for Apricot Angles Inc's EPS to reach $4.85 from $1.20 at a growth rate of 7.75%, we use the formula for compound growth. After inputting the values and solving for the number of years, it is found to be approximately 14.2 years.

Step-by-step explanation:

To determine how many years it would take for Apricot Angles Inc's earnings per share (EPS) to reach $4.85 with a consistent growth rate of 7.75% per year, we can use the formula for compound growth. The formula is given by Future Value = Present Value * (1 + Growth Rate)^Number of Years. Substituting the given values into the formula, we have $4.85 = $1.20 * (1 + 0.0775)^Number of Years. We need to solve for the Number of Years.

To find the Number of Years, we divide both sides by $1.20 and take the natural logarithm (ln) of both sides to remove the exponent, which gives us ln($4.85/$1.20) / ln(1 + 0.0775) = Number of Years. Using a calculator, the left side yields approximately 14.2, which is the Number of Years needed for the EPS to reach $4.85.