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

Answer:

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

Step-by-step 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

          $A = P(1 + \frac{r}{100} )^n$

 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

      $A = P(1 + \frac{r}{100} )^n$

       $10.5 = 3.5(1 + \frac{7}{100} )^n$

       $10.5 = 3.225^n$

Taking log of both sides

       $log 10.5 = nlog 3.225$

        $1.0212 = n(0.5085)$

         $n = \frac{1.0212}{(0.5085)}$

         $n = 2 \ years$