Question

Ten years ago, Lucas Inc. earned $0.50 per share. Its earnings this year were $5.00. What was the growth rate in earnings per share (EPS) over the 10-year period?
a. 19.42%
b. 25.89%
c. 29.78%
d. 21.75%

Answer 1

Answer:

• Option b. 25.89%

Explanation:

The question requires to calculate the annual percentage growth rate assuming it was constant.

The final earnings are equal to the initial earnings multiplied by 1 + the growth rate, raised to the number of periods.

Here:

• initial earnings = $0.50
• final earnings = $5.00
• number of periods = 10 years

Then, your equation is:

• $5.00 = $0.50 (1 + rate)¹⁰

Solving, you get:

      $(1+rate)^{10}=5/0.50\\\\(1+rate)^{10}=10\\\\(1+rate)=10^{(1/10)}\\\\1+rate=10^{0.1}\\\\1+rate=1.2589\\\\rate=1.2589-1\\\\rate=0.2589\\\\rate=25.89\%$

Thus, the answer is the option b. 25.89%