Certainly! Let's determine the rate at which the Earnings Per Share (EPS) of ABC Ltd. grew annually over the past 10 years.
1. Identify the known values:
- EPS 10 years ago: [tex]\( \text{EPS}_{\text{10\ years\ ago}} = 5 \)[/tex] Rs/share
- EPS this year: [tex]\( \text{EPS}_{\text{this\ year}} = 22 \)[/tex] Rs/share
- Number of years: [tex]\( t = 10 \)[/tex]
2. Use the formula for Compound Annual Growth Rate (CAGR):
[tex]\[
\text{CAGR} = \left(\frac{\text{EPS}_{\text{this\ year}}}{\text{EPS}_{\text{10\ years\ ago}}}\right)^{\frac{1}{t}} - 1
\][/tex]
This formula helps us determine the fixed annual growth rate that would take the EPS from its value 10 years ago to its current value.
3. Substitute the given values into the formula:
[tex]\[
\text{CAGR} = \left(\frac{22}{5}\right)^{\frac{1}{10}} - 1
\][/tex]
4. Compute the ratio and then raise it to the power of [tex]\(\frac{1}{10}\)[/tex]:
[tex]\[
\frac{22}{5} = 4.4
\][/tex]
Now we need to compute [tex]\( 4.4^{\frac{1}{10}} \)[/tex].
5. Find the 10th root of 4.4:
This requires using a calculator:
[tex]\[
4.4^{\frac{1}{10}} \approx 1.159698959
\][/tex]
6. Subtract 1 from this result to find the growth rate:
[tex]\[
1.159698959 - 1 = 0.159698959
\][/tex]
7. Convert the decimal result to a percentage:
[tex]\[
0.159698959 \times 100 \approx 15.97\%
\][/tex]
8. Compare this result to the given options and select the closest one:
- (A) 15.97%
- (B) 16.77%
- (C) 18.64%
- (D) 14.79%
The calculated Compound Annual Growth Rate (CAGR) is approximately [tex]\( 15.97\% \)[/tex].
Therefore, the correct answer is:
(A) 15.97%
