Question

Brockman Corporation's earnings per share were $3.50 last year, and its growth rate during the prior 5 years was 9.2% 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. 4.98
b. 14.98
c. 12.48
d. 7.48
e. 9.98

Answer 1

Answer:

c. 12.48

Step-by-step explanation:

The earnings per share after t years can be modeled by the following equation:

$E(t) = E(0)(1+r)^{t}$

In which E(0) is the earnings last year and r is the growth rate, as a decimal.

Brockman Corporation's earnings per share were $3.50 last year, and its growth rate during the prior 5 years was 9.2% per year. Growth rate maintained.

This means that $E(0) = 3.50, r = 0.092$

So

$E(t) = E(0)(1+r)^{t}$

$E(t) = 3.50(1+0.092)^{t}$

$E(t) = 3.50(1.092)^{t}$

If that growth rate were maintained, how many years would it take for Brockman's EPS to triple?

This is t for which E(t) = 3*E(0) = 3*3.50 = 10.50.

So

$E(t) = 3.50(1.092)^{t}$

$10.50 = 3.50(1.092)^{t}$

$(1.092)^{t} = \frac{10.50}{3.50}$

$(1.092)^{t} = 3$

$\log{(1.092)^{t}} = \log{3}$

$t\log{1.092} = \log{3}$

$t = \frac{\log{3}}{\log{1.092}}$

$t = 12.48$

So the correct answer is:

c. 12.48