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NISM Certifications · NISM-Series-XV: Research Analyst · Fundamentals of Research

Over four years, a company's revenue grew from Rs 100 crore to Rs 146.41 crore, growing by the same percentage every year. An analyst computes the compound annual growth rate (CAGR). Which statement is correct?

CAGR is 10%. Because 1.10 raised to the power 4 equals 1.4641, the revenue growth from Rs 100 crore to Rs 146.41 crore over four years corresponds to a compounded annual rate of 10%, not the simple average of 11.6%.

  1. ACAGR is 10%, since (146.41/100)^(1/4) = 1.10Correct
  2. BCAGR is 11.60%, being the total growth of 46.41% divided by 4
  3. CCAGR is 12%, because 146.41 is close to 100 x 1.12^4
  4. DCAGR is 9.5%, being the median of annual growth rates

Explanation

CAGR = (End/Start)^(1/n) - 1. Since 1.1^4 = 1.4641, the ratio 1.4641 raised to 1/4 is 1.10, so CAGR = 10%. Dividing total growth by 4 gives 11.6%, which is the simple average and ignores compounding. 12% would give 1.5735, so it does not reconcile.

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