The sales of a company rose from Rs. 2,00,000 in 2022 to Rs. 2,88,000 in 2024, and its profit rose from Rs. 50,000 to Rs. 60,500 over the same period. By how many percentage points does the compound annual growth rate (CAGR) of sales exceed the CAGR of profit?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10
From 2022 to 2024 is n = 2 years. The CAGR of each measure is worked from its own starting and ending values.
Sales:
\( \displaystyle \frac{288000}{200000} = 1.44 \)
\( \text{CAGR} = (\sqrt{1.44} - 1) \times 100 = (1.2 - 1) \times 100 = 20\% \)
Profit:
\( \displaystyle \frac{60500}{50000} = 1.21 \)
\( \text{CAGR} = (\sqrt{1.21} - 1) \times 100 = (1.1 - 1) \times 100 = 10\% \)
The difference is
\( 20 - 10 = 10 \)
Why the other options are incorrect
Option (1) 23 — Incorrect. This is the difference of the total growths over the two years, 44% − 21%, not of the yearly rates.
Option (2) 20 — Incorrect. This is the CAGR of sales alone.
Option (4) 11.5 — Incorrect. This is (44 − 21) ÷ 2, the difference of simple averages, which ignores compounding.