Respuesta :
Answer:
c. 12.48
Step-by-step explanation:
The earnings per share after t years can be modeled by the following equation:
[tex]E(t) = E(0)(1+r)^{t}[/tex]
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 [tex]E(0) = 3.50, r = 0.092[/tex]
So
[tex]E(t) = E(0)(1+r)^{t}[/tex]
[tex]E(t) = 3.50(1+0.092)^{t}[/tex]
[tex]E(t) = 3.50(1.092)^{t}[/tex]
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
[tex]E(t) = 3.50(1.092)^{t}[/tex]
[tex]10.50 = 3.50(1.092)^{t}[/tex]
[tex](1.092)^{t} = \frac{10.50}{3.50}[/tex]
[tex](1.092)^{t} = 3[/tex]
[tex]\log{(1.092)^{t}} = \log{3}[/tex]
[tex]t\log{1.092} = \log{3}[/tex]
[tex]t = \frac{\log{3}}{\log{1.092}}[/tex]
[tex]t = 12.48[/tex]
So the correct answer is:
c. 12.48
