Question

Brockman Corporation's earnings per share were $3.50 last year, and its growth rate during the prior 5 years was 7.0% per year. If that growth rate were maintained, how many years would it take for Brockman's EPS to triple?

Answer 1

The number of years it would take is
`n = 2 \ years`

Explanation:

From the question we are told that

The earning per share is
`P =` $3.50

The growth rate is r = 7.0%

The duration is
`t = 5 \ years`

Generally the future value is mathematically represented as

`A = P(1 + (r)/(100) )^n`

Where P is the present value

n is the time period

A is the future value which is mathematically evaluated as

`A = 3 * P`

substituting value

`A = 3 * 3.50`

`A =` $ 10.5 0

So

`A = P(1 + (r)/(100) )^n`

`10.5 = 3.5(1 + (7)/(100) )^n`

`10.5 = 3.225^n`

Taking log of both sides

`log 10.5 = nlog 3.225`

`1.0212 = n(0.5085)`

`n = (1.0212)/((0.5085))`

`n = 2 \ years`