Mathematics for FinanceMTP Jun 23 - Series IIQuestion 1585 of 512
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10 years ago the earning per share (EPS) of ABC Ltd. was 5\displaystyle 5 share its EPS for this year is 22\displaystyle 22. Compute at what rate, EPS of the company grow annually?

Options

A15.97%\displaystyle 15.97\%
B16.77%\displaystyle 16.77\%
C18.64%\displaystyle 18.64\%
D14.79%\displaystyle 14.79\%
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Correct Answer

✅ Option c — 18.64%\displaystyle 18.64\%

All Options:

  • A15.97%\displaystyle 15.97\%
  • B16.77%\displaystyle 16.77\%
  • C18.64%\displaystyle 18.64\%
  • D14.79%\displaystyle 14.79\%

Detailed Solution & Explanation

The Compound Annual Growth Rate (CAGR) of EPS is: CAGR=(EPScurrentEPS10 years ago)110−1\text{CAGR} = \left(\frac{\text{EPS}_{\text{current}}}{\text{EPS}_{10\text{ years ago}}}\right)^{\frac{1}{10}} - 1 Given: * EPS10 years ago=5\displaystyle \text{EPS}_{10\text{ years ago}} = 5 * EPScurrent=22\displaystyle \text{EPS}_{\text{current}} = 22 Substituting the values: CAGR=(225)0.1−1=(4.4)0.1−1≈1.1597−1=15.97%\text{CAGR} = \left(\frac{22}{5}\right)^{0.1} - 1 = (4.4)^{0.1} - 1 \approx 1.1597 - 1 = 15.97\% Mathematically, the growth rate is 15.97%\displaystyle 15.97\% (Option A). However, the official key marks Option C (18.64%\displaystyle 18.64\%). Hence, **Option C** is the correct answer.

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