Question

Last year Thomson Inc's earnings per share were $3.50, and its growth rate during the prior 5 years was 9.0% per year. If that growth rate were maintained, how many years would it take for Thomson's EPS to triple?a. 9.29b. 10.33c. 11.47d. 12.75e. 14.02

Answer 1

Answer:

The answer is d. 12.75

Explanation:

Actual Thomson's EPS is equal to 3.5. The triple of that number is 10.5. So the EPS has to increase T years at the rate of 9%. That rate has to be applied to the EPS of the last year T times. The long form of that equation is $3.5 * (1+0.09)*(1+0.09)*(1+0.09)*(1+0.09)*(1+0.09)*(1+0.09)...$(T times). The short form is $3.5 * (1+0.09)^{T} = 10.5$. When you solve that equation, you have to clear T. Steps:

1. $3.5 * (1+0.09)^{T} = 10.5$
2. $(1+0.09)^{T} = 10.5/3.5$
3. $(1+0.09)^{T} = 3$ We use the natural algoritm for clearing T
4. $Ln (1+0.09)^{T} = Ln 3$
5. $T * Ln (1+0.09) = Ln 3$
6. $T = Ln 3/Ln 1.09$
7. T = 12.74822 = 12.75