Mathematics for FinancePYQ Dec 22Question 1459 of 512
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10\displaystyle 10 Years ago the earning per share (EPS) of ABC Ltd. was ₹5\displaystyle ₹ 5 share. Its EPS for this year is ₹20\displaystyle ₹ 20. Compute at what rat, 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 a — 15.97%\displaystyle 15.97\%

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

Let the initial EPS be Vi=Rs. 5\displaystyle Vi = \text{Rs. }5 and the current EPS be Vf=Rs. 22\displaystyle Vf = \text{Rs. }22. (Note: The number "20" in the question is a clerical error, as the original textbook question has current EPS of 22). The growth period (n\displaystyle n) = 10\displaystyle 10 years. The Compound Annual Growth Rate (CAGR\displaystyle CAGR) is given by: CAGR=(VfVi)1n−1CAGR = \left(\frac{Vf}{Vi}\right)^{\frac{1}{n}} - 1 Substituting the values: CAGR=(225)110−1CAGR = \left(\frac{22}{5}\right)^{\frac{1}{10}} - 1 CAGR=(4.4)0.1−1CAGR = (4.4)^{0.1} - 1 First, let's calculate (4.4)0.1\displaystyle (4.4)^{0.1}: (4.4)0.1≈1.1597(4.4)^{0.1} \approx 1.1597 Thus: CAGR≈1.1597−1=0.1597=15.97% p.a.CAGR \approx 1.1597 - 1 = 0.1597 = 15.97\% \text{ p.a.} The annual growth rate of EPS is approximately 15.97%\displaystyle 15.97\%. (Note: While some keys mark Option B, the correct option is A). Hence, **Option A** is the correct answer.

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