Mathematics of FinanceMCQMTP 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 c18.64%\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\%

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Detailed Solution & Explanation

The Compound Annual Growth Rate (CAGR) of EPS is: CAGR=(EPScurrentEPS10 years ago)1101\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)0.11=(4.4)0.111.15971=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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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