Question

Last year Ellis Incs earnings per share were $3.50, and its growth rate during the prior 5 years was 9.0% per year. If that growth rate were maintained, how many years would it take for Ellis EPS to triple? Select one: a. 9.29 b. 10.33 c. 11.47 d. 12.75 e. 14.02

Answer 1

The correct option is d) 12.75

Step-by-step explanation:

Given,

The original price, P = $ 3.50,

Growth rate per year, r = 9.0% = 0.09,

So, the price after t years,

`A = P(1+r)^t`

`A=3.50(1+0.09)^t`

`A=3.50(1.09)^t`

If A = 3P = 3(3.50) = 10.5,

`10.5 = 3.50(1.09)^t`

`3=(1.09)^t`

Taking log both sides,

`\log 3 = \log(1.09)^t`

`\log 3 = t\log (1.09)`

`\implies t =(\log 3)/(\log 1.09)=12.7482\approx 12.75`

Hence, it will take 12.75 years for Ellis EPS to triple.

i.e. 'option d' is correct.