Question

17.a ROK's 2018 EPS (earnings per share) was $8, and its annual growth rate last 5 years was 8%. How long would it take to double its EPS at the same growth rate? (         ) years

17.b ROK's 2018 EPS (earnings per share) was $8, and its annual growth rate last 5 years was 10%. How long would it take to double its EPS at the same growth rate? (         ) years

(Please hand write solution show all steps No Excel)

Answer 1

We can use simple compounding formula for this question.

A = P x [1+ ( r/100)]^n
Where
A = Final amount
P = Principal amount
r = Interest rate of compounding
n = Time period of investment

17.a

We have A = Double the EPS of $8 = $8 x 2 = $16
We have Principal = ROKs 2018 EPS = $8
r = Growth rate = 8%
We need to find number of years to be taken to double the EPS from $8 to $16

Thus
$16 = $8 x [1+ ( 8/100)]^n
2 = (1.08)^n
Using Natural Logarithm law = Ln (a)^b = b Ln (a)
Ln (2) = n x Ln (1.08)
Thus n = 9.006 Years

It would take 9.006 Years to doubt the EPF from $8 to $16.

17.b

We have A = Double the EPS of $8 = $8 x 2 = $16
We have Principal = ROKs 2018 EPS = $8
r = Growth rate = 10%
We need to find number of years to be taken to double the EPS from $8 to $16

Thus
$16 = $8 x [1+ ( 10/100)]^n
2 = (1.10)^n
Using Natural Logarithm law = Ln (a)^b = b Ln (a)
Ln (2) = n x Ln (1.10)
Thus n = 7.273 Years

It would take 7.273 Years to doubt the EPF from $8 to $16.