Question

Brockman Corporation's earnings per share were $3.50 last year, and its growth rate during the prior 5 years was 10.0% per year. If that growth rate were maintained, how many years would it take for Brockman's EPS to triple?

Select the correct answer.

a. 16.53

b. 9.03

c. 6.53

d. 14.03

e. 11.53

Answer 1

Brockman Corporation's earnings per share were $3.50 last year

Brockman's EPS to triple; earnings per share will be 3* $3.50 = $10.50

Now we can use present value to future value formula to calculate the time period in following manner -

PV = FV/ (1+i) ^n

Where,

Present Value (PV) of earnings per share = $3.50

Future value (FV) of earnings per share (triple of the last year’s earnings per share) = 3 *$3.50 =$10.50

Annual growth rate i = 10% or 0.1

Time period n =?

Therefore,

$3.50 = $10.50/ (1+10%) ^n

Or $10.50 / $3.50 = (1.10) ^n

Or 3 = (1.10) ^n

Taking natural log from both sides

Ln (3) = n Ln (1.10)

Or n = Ln (3) / Ln (1.10)           

Or n = 1.0986/0.0953                   [use the natural log function either in excel or in calculator]

Or n = 11.53 years

Therefore it will take 11.53 years to Brockman's EPS to triple

Therefore correct answer is option e. 11.53