Mathematics for FinancePYQ Sep 24Question 1563 of 512
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The Earning Per Share (EPS) of a company for five years is given below:YearEPS201940202025202140202240202390Calculate the Compounded Annual Growth Rate (CAGR) of EPS

Options

A23.47%\displaystyle 23.47\%
B24.47%\displaystyle 24.47\%
C22.47%\displaystyle 22.47\%
D21.47%\displaystyle 21.47\%
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Correct Answer

✅ Option c — 22.47%\displaystyle 22.47\%

All Options:

  • A23.47%\displaystyle 23.47\%
  • B24.47%\displaystyle 24.47\%
  • C22.47%\displaystyle 22.47\%
  • D21.47%\displaystyle 21.47\%

Detailed Solution & Explanation

The Compound Annual Growth Rate (CAGR) of EPS is: CAGR=(EPS2023EPS2019)1n−1\text{CAGR} = \left(\frac{\text{EPS}_{2023}}{\text{EPS}_{2019}}\right)^{\frac{1}{n}} - 1 Given: * EPS2019=40\displaystyle \text{EPS}_{2019} = 40 * EPS2023=90\displaystyle \text{EPS}_{2023} = 90 * Time (n\displaystyle n) = 2023−2019=4\displaystyle 2023 - 2019 = 4 years Substituting the values: CAGR=(9040)14−1=(2.25)0.25−1≈1.2247−1=22.47%\text{CAGR} = \left(\frac{90}{40}\right)^{\frac{1}{4}} - 1 = (2.25)^{0.25} - 1 \approx 1.2247 - 1 = 22.47\% Hence, **Option C** is the correct answer.

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